Equation 677 Database

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Magma 888cebcf1adc…

magma 888cebcf1adc
Size
705
Isomorphism class hash
888cebcf1adcc1f4648c1691e86cabdc739fb3834d513bf73d563be05934b27c
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 17:41:01
Display reorder
660,75,603,609,613,602,76,623,629,633,622,77,649,653,642,643,583,74,589,593,582,543,72,549,553,542,563,73,569,573,562,423,429,81,433,422,444,448,82,452,443,463,469,83,473,462,489,483,80,493,482,509,503,78,513,502,529,523,79,533,522,691,694,696,703,29,614,601,616,600,27,634,621,636,620,28,640,656,641,654,594,25,580,596,581,554,26,541,556,540,574,24,561,576,560,434,421,35,436,420,453,442,33,455,441,474,460,34,476,461,480,494,31,496,481,500,514,32,516,501,520,534,30,536,521,695,690,698,692,160,155,369,143,187,161,153,370,141,188,159,371,142,186,154,151,156,368,139,190,152,157,366,140,191,150,158,367,138,189,146,360,166,134,185,144,361,167,132,183,145,362,165,133,184,363,149,162,137,181,364,147,163,135,182,365,148,164,136,180,683,677,669,661,256,233,297,223,309,257,231,298,224,310,255,299,222,311,232,229,252,296,226,308,230,253,294,227,306,228,254,295,225,307,239,288,262,221,300,237,289,263,219,301,238,290,261,220,302,291,235,258,217,303,292,236,259,218,304,293,234,260,216,305,680,663,666,664,2,605,617,604,606,1,625,637,624,626,0,657,644,646,645,585,5,597,584,586,545,3,557,544,546,565,4,577,564,566,425,437,8,424,426,445,459,6,457,458,465,477,7,464,466,497,485,11,484,486,517,505,9,504,506,537,525,10,524,526,700,685,704,687,205,619,607,615,618,206,639,627,635,638,204,647,655,658,659,599,208,587,595,598,559,209,547,555,558,579,207,567,575,578,439,427,211,435,438,440,446,212,454,456,479,467,210,475,478,487,499,214,495,498,507,519,215,515,518,527,539,213,535,538,693,702,688,701,119,611,610,608,612,117,631,630,628,632,118,650,648,652,651,591,115,590,588,592,551,116,550,548,552,571,114,570,568,572,431,430,110,428,432,450,449,108,447,451,471,470,109,468,472,490,491,113,488,492,510,511,111,508,512,530,531,112,528,532,697,699,689,686,168,266,285,417,333,169,264,286,418,334,170,287,419,335,265,269,171,284,416,332,267,172,282,414,330,268,173,283,415,331,272,276,174,408,324,270,277,175,409,325,271,278,176,410,326,279,275,177,411,327,280,273,178,412,328,281,274,179,413,329,684,662,676,673,202,101,71,89,321,203,99,69,87,322,201,70,88,323,100,97,198,67,85,320,98,199,68,86,318,96,200,66,84,319,107,62,193,95,312,105,60,194,93,313,106,61,192,94,314,65,103,196,91,315,63,104,197,92,316,64,102,195,90,317,670,675,667,665,56,247,345,381,39,54,248,346,382,40,55,347,383,41,246,250,59,344,380,38,251,57,342,378,36,249,58,343,379,37,245,336,51,372,45,243,337,52,373,46,244,338,53,374,47,339,241,50,375,44,340,242,48,376,42,341,240,49,377,43,678,668,672,681,126,405,357,15,393,127,406,358,16,394,128,359,17,395,407,404,129,356,14,392,402,130,354,12,390,403,131,355,13,391,396,348,124,21,384,397,349,125,22,385,398,350,123,23,386,351,399,120,20,387,352,400,121,18,388,353,401,122,19,389,674,671,679,682 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#5e8db79a467cc4283015956475779111852195ee797ae26ed1a0610c426b851f, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 17:41:02 · history