Equation 677 Database

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Magma 31755420b9bb…

magma 31755420b9bb
Size
705
Isomorphism class hash
31755420b9bbf2db2c0dd7888a52c74956e43c8fc989875e8c7dbfbe81a5dbd6
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 15:13:19
Display reorder
660,584,173,596,560,572,585,174,597,561,573,586,172,598,562,574,587,176,599,563,575,177,588,600,564,576,175,589,601,565,577,590,179,602,566,578,591,180,603,567,579,592,178,604,568,580,182,593,605,569,581,183,594,606,570,582,181,595,607,571,583,687,688,686,685,340,123,352,364,328,341,121,353,365,329,342,122,354,366,330,343,119,355,367,331,120,344,356,368,332,118,345,357,369,333,346,114,358,370,334,347,112,359,371,335,348,113,360,372,336,117,349,361,373,337,115,350,362,374,338,116,351,363,375,339,703,704,701,702,551,167,522,529,537,552,168,523,527,538,553,166,521,528,536,550,170,518,525,540,171,548,519,526,541,169,549,520,524,539,557,165,513,535,543,558,163,514,533,544,559,164,512,534,542,161,556,516,531,546,162,554,517,532,547,160,555,515,530,545,671,672,670,669,384,111,393,194,199,382,109,391,195,200,383,110,392,193,201,387,107,389,190,198,108,385,390,191,196,106,386,388,192,197,379,102,399,185,205,380,100,397,186,206,381,101,398,184,207,105,378,395,188,204,103,376,396,189,202,104,377,394,187,203,679,680,678,677,421,214,433,445,402,422,215,434,446,400,423,216,435,447,401,420,217,432,444,405,218,418,430,442,403,219,419,431,443,404,412,212,424,436,408,413,213,425,437,406,414,211,426,438,407,208,415,427,439,411,209,416,428,440,409,210,417,429,441,410,692,691,690,689,137,468,152,87,275,138,466,153,88,276,136,467,151,89,274,140,471,148,86,278,469,141,149,84,279,470,139,150,85,277,143,463,158,93,273,144,464,159,94,271,142,465,157,95,272,462,146,154,92,269,460,147,155,90,270,461,145,156,91,268,699,700,698,697,18,6,32,39,48,19,7,30,40,49,20,8,31,41,50,21,9,35,38,51,10,22,33,36,52,11,23,34,37,53,16,4,27,45,54,17,5,28,46,55,15,3,29,47,56,1,12,26,44,57,0,13,24,42,58,2,14,25,43,59,663,664,662,661,646,291,609,625,632,644,289,610,623,633,645,290,608,624,634,649,287,612,621,635,288,647,613,622,636,286,648,611,620,637,652,282,615,631,638,650,280,616,629,639,651,281,614,630,640,285,655,618,627,641,283,653,619,628,642,284,654,617,626,643,682,683,684,681,503,66,479,98,492,501,67,480,99,493,502,68,478,97,494,505,69,482,96,491,70,658,656,657,659,71,504,481,483,490,508,64,477,484,498,506,65,475,485,499,507,63,476,486,500,60,511,473,487,497,61,509,474,488,495,62,510,472,489,496,695,696,693,694,260,453,223,232,245,261,451,224,233,246,259,452,225,234,244,256,449,222,235,248,450,257,220,236,249,448,258,221,237,247,266,459,229,238,251,267,457,230,239,252,265,458,231,240,250,455,262,228,241,254,456,263,226,242,255,454,264,227,243,253,667,668,665,666,309,135,317,72,300,307,133,318,73,298,308,134,316,74,299,305,131,320,75,303,132,306,321,76,301,130,304,319,77,302,315,126,323,78,295,313,124,324,79,296,314,125,322,80,297,129,311,326,81,294,127,312,327,82,292,128,310,325,83,293,675,676,673,674 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#0c204955552ad126415d2d3170da1bc3e83549814dfd47378340ca39d32aede4, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 15:13:22 · history