Equation 677 Database

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Magma 6aef0685d475…

magma 6aef0685d475
Size
705
Isomorphism class hash
6aef0685d47554d61f174e5e1faa5e3cd135760aa0a78bf76f1b096e2446e6f3
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 17:32:14
Display reorder
660,381,369,405,159,535,379,367,403,160,533,380,368,404,158,534,372,384,408,155,538,370,382,406,156,536,371,383,407,157,537,375,387,165,411,541,373,385,166,409,539,374,386,164,410,540,390,378,161,414,544,388,376,162,412,542,389,377,163,413,543,676,681,675,673,252,237,232,77,547,253,238,233,78,545,254,239,231,79,546,240,251,235,80,550,241,249,236,81,548,242,250,234,82,549,243,258,75,230,553,244,259,76,228,551,245,260,74,229,552,257,246,71,226,556,255,247,72,227,554,256,248,73,225,555,670,668,672,664,499,440,0,169,130,497,438,2,167,128,498,439,1,168,129,443,502,4,172,126,441,500,5,170,127,442,501,3,171,125,446,505,175,7,121,444,503,173,8,119,445,504,174,6,120,508,449,178,10,124,506,447,176,11,122,507,448,177,9,123,679,685,680,678,195,417,204,68,559,196,415,202,69,557,197,416,203,70,558,420,194,207,67,562,418,192,205,65,560,419,193,206,66,561,423,199,59,210,565,421,200,60,208,563,422,201,61,209,564,653,655,62,656,657,198,424,63,211,566,191,425,64,212,567,703,702,699,704,511,298,288,50,273,509,299,289,51,274,510,297,290,52,275,301,514,287,49,276,302,512,285,47,277,300,513,286,48,278,304,517,56,294,279,305,515,57,295,280,303,516,58,296,281,520,307,55,293,282,518,308,53,291,283,519,306,54,292,284,694,691,693,689,523,34,87,141,182,521,35,88,142,183,522,33,86,140,184,30,526,83,137,181,31,524,84,138,179,32,525,85,139,180,25,529,132,93,188,26,527,133,94,189,24,528,131,92,190,532,28,135,89,187,530,29,136,90,185,531,27,134,91,186,665,666,667,662,317,452,487,113,328,315,450,485,114,329,316,451,486,115,327,455,320,490,116,331,453,318,488,117,332,454,319,489,118,330,458,312,111,493,326,456,313,112,491,324,457,314,110,492,325,311,461,107,496,322,309,459,108,494,323,310,460,109,495,321,692,695,696,690,582,428,606,397,642,580,426,604,398,640,581,427,605,399,641,431,585,609,400,645,429,583,607,401,643,430,584,608,402,644,434,588,395,612,648,432,586,396,610,646,433,587,394,611,647,591,437,391,615,651,589,435,392,613,649,590,436,393,614,650,686,688,684,677,476,40,347,340,358,474,41,345,341,356,475,42,346,339,357,39,479,350,343,361,37,477,348,344,359,38,478,349,342,360,46,482,338,353,364,44,480,336,351,362,45,481,337,352,363,659,658,334,652,654,483,43,335,354,365,484,36,333,355,366,698,700,697,701,464,594,267,223,630,462,592,268,224,628,463,593,269,222,629,597,467,270,219,633,595,465,271,220,631,596,466,272,221,632,600,470,214,265,636,598,468,215,266,634,599,469,213,264,635,473,603,217,261,639,471,601,218,262,637,472,602,216,263,638,661,671,663,669,148,618,23,103,570,146,616,21,101,568,147,617,22,102,569,621,144,19,106,573,619,145,20,104,571,620,143,18,105,572,624,154,98,14,576,622,152,99,12,574,623,153,100,13,575,150,627,97,17,579,151,625,95,15,577,149,626,96,16,578,682,683,674,687 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#58758ff0293182d6dd53be73984d3e209a66569482d3b8502bf477ddaee58f10, 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 17:32:16 · history