Equation 677 Database

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Magma 8a21b30568f4…

magma 8a21b30568f4
Size
720
Isomorphism class hash
8a21b30568f46a45bbceff14c6f055df6586f54d1077a9f5d98e234b79dda854
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
2026-10-06 18:48:17
Display reorder
23,24,25,26,27,28,29,15,16,17,18,19,20,21,22,719,462,467,444,463,468,445,464,469,446,450,470,447,451,471,448,452,472,449,453,473,435,454,474,436,455,475,437,456,476,438,457,477,439,458,478,440,459,479,441,460,465,442,461,466,443,426,433,434,420,421,422,423,424,425,428,429,430,431,432,427,690,687,689,688,221,225,203,222,226,204,223,227,205,224,228,206,210,229,207,211,230,208,212,231,209,213,232,195,214,233,196,215,234,197,216,235,198,217,236,199,218,237,200,219,238,201,220,239,202,186,193,194,180,181,182,183,184,185,188,189,190,191,192,187,681,682,680,679,497,5,494,498,6,480,499,7,481,500,8,482,501,9,483,502,10,484,503,11,485,504,12,486,505,13,487,506,14,488,507,1,489,508,0,490,509,2,491,495,3,492,496,4,493,661,662,663,664,665,666,667,668,669,670,660,673,674,672,671,700,701,699,702,573,591,628,574,592,629,575,593,615,576,594,616,577,595,617,578,596,618,579,597,619,580,598,620,581,599,621,582,585,622,583,586,623,584,587,624,570,588,625,571,589,626,572,590,627,611,603,604,605,606,607,608,609,610,613,614,600,601,602,612,716,718,715,717,84,43,66,85,44,67,86,30,68,87,31,69,88,32,70,89,33,71,75,34,72,76,35,73,77,36,74,78,37,60,79,38,61,80,39,62,81,40,63,82,41,64,83,42,65,49,56,57,58,59,45,46,47,48,51,52,53,54,55,50,706,704,705,703,339,358,320,340,359,321,341,345,322,342,346,323,343,347,324,344,348,325,330,349,326,331,350,327,332,351,328,333,352,329,334,353,315,335,354,316,336,355,317,337,356,318,338,357,319,303,310,311,312,313,314,300,301,302,305,306,307,308,309,304,678,675,677,676,108,127,90,109,128,91,110,129,92,111,130,93,112,131,94,113,132,95,114,133,96,115,134,97,116,120,98,117,121,99,118,122,100,119,123,101,105,124,102,106,125,103,107,126,104,147,139,140,141,142,143,144,145,146,149,135,136,137,138,148,709,707,710,708,563,520,544,564,521,545,565,522,546,566,523,547,567,524,548,568,510,549,569,511,550,555,512,551,556,513,552,557,514,553,558,515,554,559,516,540,560,517,541,561,518,542,562,519,543,526,533,534,535,536,537,538,539,525,528,529,530,531,532,527,696,697,695,698,165,634,160,166,635,161,167,636,162,168,637,163,169,638,164,170,639,150,171,640,151,172,641,152,173,642,153,174,643,154,175,644,155,176,630,156,177,631,157,178,632,158,179,633,159,653,645,646,647,648,649,650,651,652,655,656,657,658,659,654,712,711,714,713,272,290,268,273,291,269,274,292,255,275,293,256,276,294,257,277,295,258,278,296,259,279,297,260,280,298,261,281,299,262,282,285,263,283,286,264,284,287,265,270,288,266,271,289,267,251,243,244,245,246,247,248,249,250,253,254,240,241,242,252,685,683,686,684,413,373,394,414,374,395,415,360,396,416,361,397,417,362,398,418,363,399,419,364,400,405,365,401,406,366,402,407,367,403,408,368,404,409,369,390,410,370,391,411,371,392,412,372,393,377,384,385,386,387,388,389,375,376,379,380,381,382,383,378,691,694,692,693 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#aa78455ebb848599b7eed3f4eaf5b78527cf031421ada84aeadde26b952ffb1a, M = {0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 77} 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 2026-10-06 18:48:19 · history