Equation 677 Database

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Magma 7b3c23e06b25…

magma 7b3c23e06b25
Size
705
Isomorphism class hash
7b3c23e06b2527d172cc66d2452dec381172d4b5c723ea5942632ccdce421257
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 18:10:46
Display reorder
660,196,313,297,315,209,207,314,197,298,316,312,208,195,299,317,212,199,309,300,318,200,210,310,301,319,211,198,311,302,320,304,202,215,295,321,203,213,296,305,322,201,214,294,303,323,218,205,291,307,324,216,206,292,308,325,217,204,293,306,326,685,686,688,687,15,395,59,250,75,76,393,16,57,251,394,77,17,58,249,74,14,398,55,253,12,72,396,56,254,73,13,397,54,252,390,21,81,50,248,22,82,48,391,246,23,83,49,392,247,80,20,53,389,244,78,18,51,387,245,79,19,52,388,243,701,702,704,703,190,549,585,561,573,574,550,191,586,562,551,575,189,587,563,572,193,548,584,560,194,570,546,582,558,571,192,547,583,559,540,188,564,576,552,186,565,577,541,553,187,566,578,542,554,567,184,579,543,555,568,185,580,544,556,569,183,581,545,557,670,669,672,671,28,416,407,95,98,96,414,29,405,93,415,97,27,406,94,101,24,412,410,91,25,99,413,408,92,100,26,411,409,90,422,34,104,402,86,35,102,403,420,84,33,103,404,421,85,107,30,401,418,89,105,31,399,419,87,106,32,400,417,88,680,677,679,678,424,117,146,129,142,143,118,425,144,130,119,141,423,145,131,138,427,116,149,128,428,139,114,147,126,140,426,115,148,127,108,430,133,152,120,431,134,150,109,121,429,132,151,110,122,136,433,155,111,123,137,434,153,112,124,135,432,154,113,125,689,690,691,692,171,489,287,504,46,47,490,172,285,505,491,45,173,286,506,42,170,492,290,503,168,43,493,288,501,44,169,494,289,502,487,177,37,282,495,178,38,283,488,496,179,36,284,486,497,40,176,281,483,498,41,174,279,484,499,39,175,280,485,500,697,698,700,699,599,602,647,621,633,634,600,597,645,622,601,635,598,646,623,632,595,605,643,620,596,630,603,644,618,631,594,604,642,619,608,590,624,638,612,588,625,636,606,613,589,626,637,607,614,627,593,641,611,615,628,591,639,609,616,629,592,640,610,617,661,662,664,663,227,336,365,348,361,362,337,225,363,349,338,360,226,364,350,357,230,335,368,347,228,358,333,366,345,359,229,334,367,346,327,222,352,371,339,223,353,369,328,340,224,351,370,329,341,355,221,374,330,342,356,219,372,331,343,354,220,373,332,344,682,681,684,683,3,511,537,519,525,526,512,4,538,520,510,527,5,539,521,528,2,507,536,518,1,529,508,534,516,530,0,509,535,517,653,9,654,655,652,10,658,659,657,656,11,649,650,648,651,180,8,531,513,524,181,6,532,514,522,182,7,533,515,523,693,694,696,695,165,441,474,457,459,460,442,166,475,458,443,461,167,476,456,462,164,444,473,453,162,463,445,471,454,464,163,446,472,455,439,156,465,480,448,157,466,481,440,449,158,467,482,438,447,468,159,479,435,451,469,160,477,436,452,470,161,478,437,450,666,665,668,667,242,269,256,70,381,382,267,240,257,71,268,383,241,255,69,384,238,272,259,66,239,385,270,260,67,386,237,271,258,68,275,233,379,262,61,231,380,263,273,62,232,378,261,274,60,375,236,265,278,64,376,234,266,276,65,377,235,264,277,63,674,673,676,675 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#6997491de262e367994a4a50c6f8055cb54c2a6a0260cea123f554e749c551e0, 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 18:10:47 · history