Equation 677 Database

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Magma 6d10d314cce3…

magma 6d10d314cce3
Size
720
Isomorphism class hash
6d10d314cce3568ace816583267f8802a9cb4d0ed36768a36ccf33fff778701c
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 719) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 07:30:24
Display reorder
556,557,558,559,560,561,562,563,564,565,566,567,568,569,555,719,177,141,162,178,142,163,179,143,164,165,144,150,166,145,151,167,146,152,168,147,153,169,148,154,170,149,155,171,135,156,172,136,157,173,137,158,174,138,159,175,139,160,176,140,161,188,180,181,182,183,184,185,186,187,190,191,192,193,194,189,690,688,689,687,354,317,338,355,318,339,356,319,340,357,320,341,358,321,342,359,322,343,345,323,344,346,324,330,347,325,331,348,326,332,349,327,333,350,328,334,351,329,335,352,315,336,353,316,337,365,372,373,374,360,361,362,363,364,367,368,369,370,371,366,681,682,680,679,1,195,217,0,196,218,2,197,219,3,198,220,4,199,221,5,200,222,6,201,223,7,202,224,8,203,210,9,204,211,10,205,212,11,206,213,12,207,214,13,208,215,14,209,216,661,662,663,664,665,666,667,668,669,670,660,673,674,672,671,700,702,699,701,576,607,628,577,608,629,578,609,615,579,610,616,580,611,617,581,612,618,582,613,619,583,614,620,584,600,621,570,601,622,571,602,623,572,603,624,573,604,625,574,605,626,575,606,627,589,596,597,598,599,585,586,587,588,591,592,593,594,595,590,716,717,715,718,448,476,484,449,477,485,435,478,486,436,479,487,437,465,488,438,466,489,439,467,490,440,468,491,441,469,492,442,470,493,443,471,494,444,472,480,445,473,481,446,474,482,447,475,483,459,451,452,453,454,455,456,457,458,461,462,463,464,450,460,705,704,706,703,42,71,27,43,72,28,44,73,29,30,74,15,31,60,16,32,61,17,33,62,18,34,63,19,35,64,20,36,65,21,37,66,22,38,67,23,39,68,24,40,69,25,41,70,26,54,46,47,48,49,50,51,52,53,56,57,58,59,45,55,678,676,677,675,554,518,539,540,519,525,541,520,526,542,521,527,543,522,528,544,523,529,545,524,530,546,510,531,547,511,532,548,512,533,549,513,534,550,514,535,551,515,536,552,516,537,553,517,538,499,506,507,508,509,495,496,497,498,501,502,503,504,505,500,709,708,710,707,258,234,242,259,235,243,260,236,244,261,237,245,262,238,246,263,239,247,264,225,248,265,226,249,266,227,250,267,228,251,268,229,252,269,230,253,255,231,254,256,232,240,257,233,241,284,276,277,278,279,280,281,282,283,271,272,273,274,275,270,696,698,695,697,642,286,307,643,287,308,644,288,309,630,289,310,631,290,311,632,291,312,633,292,313,634,293,314,635,294,300,636,295,301,637,296,302,638,297,303,639,298,304,640,299,305,641,285,306,653,645,646,647,648,649,650,651,652,655,656,657,658,659,654,712,713,714,711,414,376,397,415,377,398,416,378,399,417,379,400,418,380,401,419,381,402,405,382,403,406,383,404,407,384,390,408,385,391,409,386,392,410,387,393,411,388,394,412,389,395,413,375,396,425,432,433,434,420,421,422,423,424,427,428,429,430,431,426,685,684,686,683,96,124,81,97,125,82,98,126,83,99,127,84,100,128,85,101,129,86,102,130,87,103,131,88,104,132,89,90,133,75,91,134,76,92,120,77,93,121,78,94,122,79,95,123,80,107,114,115,116,117,118,119,105,106,109,110,111,112,113,108,691,693,692,694 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 720 = 16 + 11*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 11, B) with E = magma#5e76c6d3b965544f3246a1396d58a622a92ac5abe1044f6db52aefba39d6a87c, M = {0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 57, 75} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 45.

last edited by qawbecrdtey at 2026-10-08 07:30:39 · history