Equation 677 Database

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Magma 24add5754ff1…

magma 24add5754ff1
Size
705
Isomorphism class hash
24add5754ff19b09b66d585239711261aeaf421d22ec95b79534fa491d7afe28
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 16:00:13
Display reorder
660,398,455,148,346,530,347,456,399,149,531,345,454,397,150,529,458,394,147,349,533,145,395,459,350,534,396,457,146,348,532,453,154,389,344,528,451,155,390,342,526,452,156,388,343,527,449,153,392,340,524,450,151,393,341,525,152,448,391,339,523,676,686,685,681,72,184,204,373,354,374,185,70,202,355,372,186,71,203,356,183,68,200,369,353,201,69,181,370,351,67,182,199,371,352,190,195,63,364,360,191,193,61,365,361,192,194,62,363,362,189,198,66,367,359,187,196,64,368,357,197,188,65,366,358,668,665,672,669,82,479,443,382,215,383,480,83,444,216,381,478,84,442,214,482,81,446,385,211,447,79,483,386,212,80,481,445,384,213,477,441,73,380,206,475,439,74,378,207,476,440,75,379,205,473,437,76,376,209,474,438,77,377,210,436,472,78,375,208,677,679,680,682,234,623,624,621,620,629,631,232,632,628,612,615,233,616,613,647,230,648,644,645,656,231,655,653,652,229,639,640,636,637,607,608,240,604,605,591,592,238,589,588,599,600,239,597,596,572,573,236,577,576,583,584,237,581,580,1,520,235,278,277,704,700,698,703,262,306,159,407,419,408,307,263,157,420,406,308,264,158,418,305,261,162,410,422,160,259,303,411,423,260,304,161,409,421,312,165,253,405,417,313,163,254,403,415,314,164,255,404,416,311,168,256,401,413,309,166,257,402,414,167,310,258,400,412,691,693,692,694,269,431,217,467,22,468,432,270,218,23,466,430,268,219,24,434,265,220,470,21,221,266,435,471,19,267,433,222,469,20,429,223,275,465,13,427,224,276,463,14,428,225,274,464,15,425,226,271,461,16,426,227,272,462,17,228,424,273,460,18,664,661,667,663,177,90,100,122,118,123,88,175,101,119,121,89,176,102,120,86,180,99,125,117,97,178,87,126,115,179,85,98,124,116,96,106,172,128,109,94,107,173,129,110,95,108,174,127,111,92,105,171,131,112,93,103,169,132,113,104,91,170,130,114,690,695,696,689,141,50,567,334,47,335,51,139,568,48,333,49,140,566,46,53,144,570,337,43,571,142,54,338,44,143,52,569,336,45,56,565,136,332,38,57,563,137,330,39,55,564,138,331,37,59,561,135,328,41,60,562,133,329,42,560,58,134,327,40,675,688,678,674,29,622,625,626,627,634,630,30,633,635,618,614,28,617,619,646,25,649,650,651,657,26,654,658,659,27,638,641,642,643,606,609,35,610,611,590,593,36,594,595,598,601,34,602,603,578,579,31,574,575,582,585,32,586,587,521,387,33,522,535,701,699,702,697,246,555,503,295,284,296,556,244,504,282,294,554,245,502,283,558,242,506,291,280,507,243,559,292,281,241,557,505,293,279,553,501,252,301,290,551,499,250,302,288,552,500,251,300,289,549,497,248,297,286,550,498,249,298,287,496,548,247,299,285,662,666,670,671,2,515,543,322,491,323,516,3,544,492,321,514,0,542,490,518,5,546,325,494,547,6,519,326,495,4,517,545,324,493,513,541,8,320,489,511,539,9,318,487,512,540,7,319,488,509,537,11,316,485,510,538,12,317,486,536,508,10,315,484,673,687,683,684 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#2c9cca33fbeafeb683cb8962a04870775a8e5c306e9c00d15364712f8c215d93, 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 16:00:14 · history