Equation 677 Database

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Magma 85e0e8838613…

magma 85e0e8838613
Size
705
Isomorphism class hash
85e0e88386139d8b93451d5b62dc2a1cb87d4a2b14ab06ea38aa5c4f6a0e66bc
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 21:45:23
Display reorder
660,57,484,400,526,230,58,485,527,401,228,483,525,59,399,229,56,480,522,396,233,54,481,523,397,231,55,482,524,398,232,490,406,63,532,236,491,407,64,533,234,489,405,65,531,235,486,402,62,528,239,403,487,60,529,237,488,404,61,530,238,676,681,686,678,304,79,412,460,330,305,80,461,413,331,78,459,303,411,332,300,82,456,408,333,301,83,457,409,334,302,81,458,410,335,85,418,310,466,328,86,419,311,467,329,84,417,309,465,327,88,414,306,462,324,415,89,307,463,325,87,416,308,464,326,662,665,661,663,247,340,424,502,544,248,341,503,425,545,339,501,246,423,543,250,336,498,420,540,251,337,499,421,541,249,338,500,422,542,346,430,245,508,550,347,431,243,509,551,345,429,244,507,549,342,426,241,504,546,427,343,242,505,547,344,428,240,506,548,677,679,682,673,264,388,92,538,495,265,389,539,90,496,387,537,266,91,497,267,384,534,95,494,268,385,535,93,492,269,386,536,94,493,646,645,270,649,648,654,652,271,657,656,638,637,272,641,640,614,613,273,617,616,620,622,274,625,624,630,628,275,633,632,703,700,699,704,185,514,472,436,556,183,515,437,473,557,513,435,184,471,555,181,510,432,468,552,182,511,433,469,553,180,512,434,470,554,520,478,191,442,562,521,479,189,443,563,519,477,190,441,561,516,474,187,438,558,475,517,188,439,559,518,476,186,440,560,692,691,694,693,161,372,252,568,21,159,373,569,253,22,374,567,160,254,23,157,375,564,255,20,158,376,565,256,18,156,377,566,257,19,378,258,167,574,12,379,259,165,575,13,380,260,166,573,14,381,261,163,570,15,262,382,164,571,16,383,263,162,572,17,668,671,666,669,352,116,125,34,132,353,114,35,123,133,115,33,351,124,134,348,119,30,121,135,349,117,31,122,136,350,118,32,120,137,111,131,358,25,138,112,129,359,26,139,113,130,357,24,140,110,127,354,28,141,128,108,355,29,142,109,126,356,27,143,689,695,696,690,154,364,6,604,586,155,365,605,7,587,363,603,153,8,585,150,360,600,9,582,151,361,601,10,583,152,362,602,11,584,370,4,145,610,592,371,5,146,611,593,369,3,144,609,591,366,1,148,606,588,0,367,149,607,589,368,2,147,608,590,674,688,685,675,69,598,393,40,580,70,599,41,394,581,597,39,71,395,579,68,594,36,392,576,66,595,37,390,577,67,596,38,391,578,651,647,75,644,650,659,655,76,653,658,643,639,77,636,642,619,618,74,612,615,623,627,72,621,626,635,631,73,629,634,697,698,701,702,170,314,285,448,293,168,312,449,286,291,313,447,169,287,292,173,317,444,284,289,171,315,445,282,290,172,316,446,283,288,320,276,176,454,299,318,277,174,455,297,319,278,175,453,298,323,279,179,450,295,280,321,177,451,296,322,281,178,452,294,672,664,667,670,46,216,100,209,200,47,217,207,101,198,218,208,45,99,199,42,219,205,96,203,43,220,206,97,201,44,221,204,98,202,222,106,52,215,195,223,107,53,213,196,224,105,51,214,197,225,102,48,211,194,103,226,49,212,192,227,104,50,210,193,687,683,680,684 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#f1e2c600ebf06c2e31b8968226514217c5fc265d2577d787fe558118ce3f2b96, 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 21:45:24 · history