Equation 677 Database

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Magma 100c89e31ae1…

magma 100c89e31ae1
Size
705
Isomorphism class hash
100c89e31ae1433cf45dacaf3413595c99f6b89cf2bd9cc41d80048887b30cb0
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 17:20:43
Display reorder
660,361,490,53,450,421,362,491,51,451,422,360,489,52,449,420,486,357,49,446,417,50,358,487,447,418,488,359,48,448,419,352,481,59,441,412,353,482,57,442,413,351,480,58,440,411,484,355,55,444,415,485,356,56,445,416,483,354,54,443,414,680,677,675,683,466,118,80,104,313,467,119,78,102,314,465,117,79,103,312,114,462,83,107,309,81,463,115,105,310,116,464,82,106,311,457,109,75,99,304,458,110,76,100,305,456,108,77,101,303,112,460,74,98,307,113,461,72,96,308,111,459,73,97,306,672,662,666,665,478,337,127,526,550,479,338,128,527,551,477,336,126,525,549,333,474,130,522,546,131,475,334,523,547,335,476,129,524,548,469,328,125,517,541,470,329,123,518,542,468,327,124,516,540,331,472,121,520,544,332,473,122,521,545,330,471,120,519,543,686,687,681,673,650,647,162,644,645,658,655,160,653,652,642,639,161,636,637,615,618,158,612,613,159,626,623,620,621,631,634,157,629,628,565,225,153,164,169,566,226,151,165,167,564,224,152,163,168,597,599,156,601,600,607,610,154,605,604,223,567,155,170,166,703,698,700,704,325,373,0,272,397,326,374,2,270,398,324,372,1,271,396,369,321,4,268,393,5,322,370,269,394,371,323,3,267,395,316,364,7,278,388,317,365,8,276,389,315,363,6,277,387,367,319,10,274,391,368,320,11,275,392,366,318,9,273,390,689,692,690,691,349,562,142,26,538,350,563,143,24,539,348,561,144,25,537,558,345,141,29,534,139,346,559,27,535,560,347,140,28,536,340,553,148,32,529,341,554,149,30,530,339,552,150,31,528,556,343,147,35,532,557,344,145,33,533,555,342,146,34,531,667,669,663,670,190,251,297,246,196,191,252,298,247,197,189,253,299,245,195,254,193,300,249,199,301,194,255,250,200,256,192,302,248,198,188,257,295,244,202,186,258,296,242,203,187,259,294,243,201,260,184,291,240,205,261,185,292,241,206,262,183,293,239,204,693,695,696,694,437,514,36,502,594,439,515,37,503,595,435,513,38,501,593,510,132,39,498,590,40,431,511,499,591,512,433,41,500,592,134,505,42,493,585,135,506,43,494,586,133,504,44,492,584,508,137,45,496,588,509,138,46,497,589,507,136,47,495,587,684,688,678,685,648,651,212,646,649,656,659,210,654,657,640,643,211,638,641,619,616,208,614,617,209,624,627,622,625,635,632,207,630,633,266,570,218,221,453,264,568,216,219,454,265,569,217,220,452,603,602,214,596,598,611,608,215,606,609,571,263,213,222,455,699,697,702,701,19,385,62,94,582,20,386,60,95,583,18,384,61,93,581,381,22,65,90,578,63,23,382,91,579,383,21,64,92,580,17,376,68,85,573,15,377,66,86,574,16,375,67,84,572,379,13,71,88,576,380,14,69,89,577,378,12,70,87,575,668,671,661,664,409,436,231,287,175,410,438,232,285,176,408,434,230,286,174,423,405,227,290,171,228,406,430,288,172,432,407,229,289,173,400,426,237,282,181,401,424,238,283,182,399,425,236,284,180,429,403,233,281,177,427,404,234,279,178,428,402,235,280,179,682,674,676,679 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#4f47b623d963c151ceba4da4fdb4170837133dc09cb743e53f258ef94ac4defc, 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 17:20:45 · history