Equation 677 Database

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Magma c8d46d0811e3…

magma c8d46d0811e3
Size
705
Isomorphism class hash
c8d46d0811e377cc37b406444995a133a50fb5f36f81b38957a64ab86d6c0c72
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 15:54:59
Display reorder
660,53,451,193,528,586,194,51,526,584,449,195,52,450,527,585,192,56,447,524,582,190,54,448,525,583,55,191,446,523,581,199,59,442,519,577,57,440,517,200,575,441,58,518,201,576,445,62,522,198,580,443,60,520,196,578,444,61,521,197,579,682,687,684,680,410,47,80,260,367,78,408,261,368,45,79,409,46,259,369,76,406,50,256,366,77,407,48,257,364,405,75,49,258,365,86,401,42,251,358,399,43,252,84,359,44,400,250,85,360,41,404,254,82,361,39,402,255,83,362,40,403,253,81,363,667,672,663,670,381,427,266,574,475,267,379,572,473,425,265,380,426,573,474,262,377,423,570,471,263,378,424,571,472,376,264,422,569,470,272,372,418,565,466,370,416,563,273,464,417,371,564,271,465,421,375,568,268,469,419,373,566,269,467,420,374,567,270,468,686,681,676,678,654,652,232,653,659,233,638,636,643,637,234,646,645,644,651,235,622,621,620,627,236,630,628,629,635,614,237,613,612,619,230,396,25,101,601,394,26,99,231,599,24,395,100,229,600,605,606,604,226,608,104,397,102,227,602,105,398,103,228,603,698,700,697,701,202,321,334,499,393,335,203,497,391,319,336,204,320,498,392,337,205,317,495,389,338,206,318,496,390,207,339,316,494,388,340,208,312,490,384,209,310,488,341,382,311,210,489,342,383,315,211,493,343,387,313,212,491,344,385,314,213,492,345,386,693,692,695,690,487,289,90,274,463,91,485,275,461,290,92,486,291,276,462,89,483,288,277,459,87,484,286,278,460,482,88,287,279,458,96,478,295,280,454,476,296,281,97,452,297,477,282,98,453,294,481,283,95,457,292,479,284,93,455,293,480,285,94,456,662,665,666,669,138,333,176,545,511,177,136,543,509,331,175,137,332,544,510,172,141,329,541,507,173,139,330,542,508,140,174,328,540,506,167,133,324,536,502,134,322,534,168,500,323,135,535,166,501,327,132,539,170,505,325,130,537,171,503,326,131,538,169,504,696,694,689,691,557,118,145,439,184,146,555,437,185,119,147,556,120,438,186,144,553,121,435,187,142,554,122,436,188,552,143,123,434,189,151,548,124,430,182,546,125,428,152,183,126,547,429,153,181,127,551,433,150,178,128,549,431,148,179,129,550,432,149,180,679,685,683,677,658,657,114,655,656,112,642,639,640,641,113,650,649,647,648,117,626,625,623,624,115,634,633,631,632,618,116,617,615,616,109,560,531,415,514,558,529,413,110,512,530,559,414,111,513,610,611,609,108,607,532,561,412,106,515,533,562,411,107,516,699,702,704,703,244,33,23,6,68,21,245,7,66,34,22,246,35,8,67,19,247,36,9,64,20,248,37,10,65,249,18,38,11,63,14,242,31,4,74,243,32,5,12,72,30,241,3,13,73,27,238,1,17,70,28,239,0,15,71,29,240,2,16,69,671,661,664,668,357,598,156,223,309,154,355,224,307,596,155,356,597,225,308,159,353,594,222,305,157,354,595,220,306,352,158,593,221,304,162,348,589,214,300,346,587,215,160,298,588,347,216,161,299,592,351,217,165,303,590,349,218,163,301,591,350,219,164,302,674,673,675,688 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#24594adec9458e953c3b7e97dafa6bb51a67ac64efb5ebe0d91d39b768cf806c, 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 15:55:02 · history