Equation 677 Database

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Magma e63469b6a34a…

magma e63469b6a34a
Size
705
Isomorphism class hash
e63469b6a34a7253e5441335ad9e784d7941d7472321bdecade0e6466c583aaa
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 15:12:31
Display reorder
660,68,48,69,333,325,66,49,70,334,326,67,71,335,324,50,47,64,72,332,328,45,65,73,330,329,46,63,74,331,327,59,54,339,75,323,57,55,340,76,321,77,58,56,341,322,53,62,338,78,319,51,60,336,79,320,52,61,337,80,318,685,686,688,687,448,429,247,415,413,449,430,245,416,411,447,246,414,412,431,428,444,243,418,409,426,445,244,419,410,427,446,242,417,408,439,435,421,238,404,440,436,422,236,402,237,438,437,420,403,434,442,424,241,407,432,443,425,239,405,433,441,423,240,406,701,702,704,703,580,579,316,604,603,581,577,317,605,601,582,315,606,602,578,575,583,312,607,599,576,584,313,608,600,574,585,314,609,598,586,570,610,307,594,587,568,611,308,592,306,588,569,612,593,573,589,613,310,597,571,590,614,311,595,572,591,615,309,596,670,669,672,671,458,156,259,141,464,456,157,257,142,462,457,258,140,463,155,152,461,255,144,467,153,459,256,145,465,154,460,254,143,466,453,162,147,250,470,454,163,148,248,468,249,455,161,146,469,158,452,150,253,473,159,450,151,251,471,160,451,149,252,472,680,677,679,678,480,521,269,501,488,481,519,270,502,486,482,271,503,487,520,517,483,268,500,491,518,484,266,498,489,516,485,267,499,490,478,512,507,260,494,479,510,508,261,492,262,477,511,509,493,515,474,506,263,497,513,475,504,264,495,514,476,505,265,496,689,690,691,692,549,541,125,198,290,550,542,123,199,291,551,124,197,292,540,544,548,128,194,293,545,546,126,195,294,543,547,127,196,295,555,539,189,120,288,556,537,190,121,289,122,557,538,188,287,535,554,192,119,284,536,552,193,117,285,534,553,191,118,286,697,698,700,699,628,622,651,82,96,629,623,649,83,97,630,650,81,98,624,625,631,647,85,95,626,632,648,86,93,627,633,646,84,94,634,620,88,642,102,635,621,89,640,103,641,636,619,87,104,616,637,91,645,101,617,638,92,643,99,618,639,90,644,100,661,662,664,663,389,369,15,356,353,387,370,16,354,351,388,17,355,352,371,368,385,14,359,349,366,386,12,357,350,367,384,13,358,348,380,375,362,21,344,378,376,360,22,342,23,379,377,361,343,374,383,365,20,347,372,381,363,18,345,373,382,364,19,346,682,681,684,683,136,302,200,32,562,134,300,201,30,563,135,202,31,564,301,305,139,203,28,565,303,137,204,29,566,304,138,205,27,567,656,658,657,206,659,129,299,133,207,561,208,653,654,652,655,298,132,26,209,560,296,130,24,210,558,297,131,25,211,559,693,694,696,695,176,172,109,274,530,177,170,110,272,528,178,108,273,529,171,175,179,105,277,533,173,180,106,275,531,174,181,107,276,532,182,167,280,115,525,183,168,278,116,526,114,184,169,279,527,166,185,283,111,524,164,186,281,112,522,165,187,282,113,523,666,665,668,667,227,219,397,41,6,228,220,398,39,7,229,396,40,8,218,222,226,400,44,9,223,224,401,42,10,221,225,399,43,11,233,217,36,395,4,234,215,37,393,5,394,235,216,38,3,213,232,35,391,1,214,230,33,392,0,212,231,34,390,2,674,673,676,675 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#0afaa5a95ac3a042540e79b2adb5184e36490c06a1d05440665a030a584e7e24, 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 15:12:34 · history