Equation 677 Database

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Magma 8d4584f1da99…

magma 8d4584f1da99
Size
705
Isomorphism class hash
8d4584f1da99cb6ef73063569df7b5cdc42d22628c7efa9526a96edc97fba31d
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 16:54:37
Display reorder
660,55,232,491,307,387,56,308,233,492,388,54,306,231,490,386,51,235,310,494,390,52,236,311,495,391,53,234,309,493,389,230,313,497,46,393,228,314,498,47,394,229,312,496,45,392,316,226,500,49,396,317,227,501,50,397,315,225,499,48,395,674,679,673,683,178,154,141,503,209,179,504,155,142,207,177,502,153,143,208,181,157,506,144,212,182,158,507,145,210,180,156,505,146,211,160,509,147,184,204,161,510,148,185,205,159,508,149,183,206,512,163,150,187,203,513,164,151,188,201,511,162,152,186,202,668,672,665,661,38,479,599,319,419,36,320,480,600,420,37,318,478,598,418,34,482,322,602,422,35,483,323,603,423,33,481,321,601,421,485,325,605,44,425,486,326,606,42,426,484,324,604,43,424,328,488,608,40,428,329,489,609,41,429,327,487,607,39,427,682,680,675,687,10,1,297,289,636,11,290,0,298,634,9,291,2,296,635,13,3,288,300,639,14,4,286,301,637,12,5,287,299,638,6,293,303,16,642,7,294,304,17,640,8,295,302,15,641,645,644,646,19,648,652,653,654,20,659,285,292,305,18,643,698,700,701,697,62,237,527,611,431,60,612,238,528,432,61,610,239,526,430,58,240,614,530,434,59,241,615,531,435,57,242,613,529,433,243,617,533,68,437,244,618,534,66,438,245,616,532,67,436,620,246,536,64,440,621,247,537,65,441,619,248,535,63,439,690,691,696,694,273,87,467,587,539,274,588,88,468,540,275,586,89,466,538,276,90,590,470,542,277,91,591,471,543,278,92,589,469,541,85,593,473,279,545,86,594,474,280,546,84,592,472,281,544,596,81,476,282,548,597,82,477,283,549,595,83,475,284,547,671,667,670,664,256,110,515,24,128,257,25,108,516,126,255,26,109,514,127,259,106,23,518,124,260,107,21,519,125,258,105,22,517,123,116,30,521,254,119,114,31,522,252,117,115,32,520,253,118,29,112,524,250,122,27,113,525,251,120,28,111,523,249,121,692,695,689,693,69,351,375,551,265,70,552,352,376,266,71,550,350,374,264,72,354,554,378,261,73,355,555,379,262,74,353,553,377,263,357,557,381,75,271,358,558,382,76,272,356,556,380,77,270,560,360,384,78,267,561,361,385,79,268,559,359,383,80,269,677,676,685,678,135,334,400,341,409,136,342,335,398,410,137,340,336,399,408,138,337,344,403,412,139,338,345,401,413,140,339,343,402,411,332,347,406,133,415,333,348,404,134,416,331,346,405,132,414,650,649,651,129,647,656,655,657,130,658,349,330,407,131,417,704,702,699,703,193,166,455,575,363,194,576,167,456,364,192,574,165,454,362,189,169,578,458,366,190,170,579,459,367,191,168,577,457,365,172,581,461,199,369,173,582,462,200,370,171,580,460,198,368,584,175,464,195,372,585,176,465,196,373,583,174,463,197,371,666,662,669,663,217,443,623,94,563,218,95,444,624,564,216,93,442,622,562,213,446,97,626,566,214,447,98,627,567,215,445,96,625,565,449,100,629,223,569,450,101,630,224,570,448,99,628,222,568,103,452,632,219,572,104,453,633,220,573,102,451,631,221,571,681,686,684,688 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#48377dacddf39e37ac6c06158aa2a2d147d932b71f91ecfb6a61a025238f8f4a, 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 16:54:39 · history