Equation 677 Database

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Magma 061951c6eced…

magma 061951c6eced
Size
705
Isomorphism class hash
061951c6eced1f8fdc45ed5a465b8d6290aad5e2ea525651f32fca68de88fa84
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 17:41:13
Display reorder
660,312,70,522,507,492,313,71,523,508,493,314,524,509,494,69,73,311,521,506,491,74,309,519,504,489,72,310,520,505,490,68,513,318,498,483,66,514,319,499,484,67,515,320,500,485,516,64,317,501,486,517,65,315,502,487,518,63,316,503,488,682,683,681,685,284,221,227,189,248,282,219,225,190,246,283,226,191,247,220,224,280,230,192,244,222,281,228,193,245,223,279,229,194,243,216,233,275,195,239,217,231,273,196,237,218,232,274,197,238,236,215,278,198,242,234,213,276,199,240,235,214,277,200,241,664,667,661,671,154,105,561,7,285,155,106,562,5,286,153,563,6,287,107,108,157,560,10,288,109,158,558,8,289,110,156,559,9,290,103,552,152,2,291,104,553,150,3,292,102,554,151,4,293,555,99,148,14,294,556,100,149,0,295,557,101,147,1,296,679,686,687,674,61,640,637,636,642,62,648,645,644,650,60,652,653,658,656,632,57,628,629,634,616,58,613,612,618,624,59,620,621,626,480,185,52,11,510,481,183,53,12,511,482,184,51,13,512,588,590,55,592,593,596,600,56,597,602,606,608,54,605,610,703,698,700,704,75,323,477,366,426,76,321,478,367,427,77,479,368,428,322,326,78,476,365,425,324,79,474,363,423,325,80,475,364,424,329,468,81,357,417,327,469,82,358,418,328,470,83,359,419,471,332,84,360,420,472,330,85,361,421,473,331,86,362,422,690,692,691,693,122,573,549,173,162,120,574,550,171,163,121,551,172,164,575,572,118,548,176,161,570,119,546,174,159,571,117,547,175,160,564,540,113,179,168,565,541,111,177,169,566,542,112,178,170,543,567,116,182,167,544,568,114,180,165,545,569,115,181,166,665,670,669,672,25,336,144,431,95,26,337,145,429,93,24,146,430,94,338,335,21,143,434,98,333,22,141,432,96,334,23,142,433,97,342,135,16,437,90,343,136,17,435,91,344,137,15,436,92,138,341,19,440,89,139,339,20,438,87,140,340,18,439,88,694,695,696,689,308,534,585,354,450,306,535,586,355,451,307,587,356,452,536,533,304,584,353,449,531,305,582,351,447,532,303,583,352,448,525,576,299,345,441,526,577,297,346,442,527,578,298,347,443,579,528,302,348,444,580,529,300,349,445,581,530,301,350,446,673,688,677,684,42,643,639,641,638,43,651,647,649,646,44,655,657,654,659,635,41,631,633,630,619,39,615,617,614,627,40,623,625,622,537,467,48,495,188,538,465,49,496,186,539,466,50,497,187,594,595,47,591,589,599,603,45,601,598,607,611,46,609,604,699,697,702,701,210,414,259,390,262,211,415,260,391,263,212,258,392,261,416,413,209,255,389,265,411,207,256,387,266,412,208,257,388,264,405,250,201,381,268,406,251,202,382,269,407,249,203,383,267,253,408,204,384,271,254,409,205,385,272,252,410,206,386,270,662,666,668,663,133,31,402,462,378,134,32,403,463,379,132,404,464,380,30,27,129,401,461,377,28,130,399,459,375,29,131,400,460,376,37,393,124,453,369,38,394,125,454,370,36,395,123,455,371,396,33,127,456,372,397,34,128,457,373,398,35,126,458,374,678,676,675,680 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 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#5e8db79a467cc4283015956475779111852195ee797ae26ed1a0610c426b851f, M = {60} 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 2026-10-03 17:41:15 · history