Equation 677 Database

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Magma c1dbcc91fa79…

magma c1dbcc91fa79
Size
705
Isomorphism class hash
c1dbcc91fa793a5e0129ce9f102aaf22f389e381b27ffcfc0281f2e42c88d768
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 15:53:59
Display reorder
660,67,66,68,69,70,71,64,65,63,60,61,62,260,258,259,263,261,262,255,256,257,254,252,253,647,645,646,643,644,642,638,636,637,641,639,640,584,582,583,587,585,586,579,580,581,578,576,577,125,123,124,121,122,120,131,129,130,127,128,126,669,683,689,684,160,159,161,158,156,157,165,166,167,164,162,163,440,438,439,443,441,442,435,436,437,434,432,433,42,43,44,45,46,47,40,41,39,36,37,38,374,372,373,377,375,376,380,378,379,383,381,382,503,501,502,499,500,498,494,492,493,497,495,496,661,673,675,672,599,598,597,594,595,596,589,590,588,592,593,591,274,275,273,270,271,272,265,266,264,268,269,267,659,657,658,655,656,654,650,648,649,653,651,652,13,14,12,16,17,15,19,20,18,22,23,21,173,171,172,169,170,168,179,177,178,175,176,174,668,678,688,685,340,339,341,338,336,337,345,346,347,344,342,343,198,199,200,201,202,203,196,197,195,192,193,194,319,320,318,322,323,321,317,315,316,313,314,312,309,310,311,308,306,307,300,301,302,303,304,305,335,333,334,331,332,330,326,324,325,329,327,328,693,704,703,700,402,404,403,407,405,406,399,400,401,398,396,397,527,525,526,523,524,522,518,516,517,521,519,520,463,464,462,466,467,465,461,459,460,457,458,456,8,6,7,11,9,10,3,4,5,2,1,0,101,99,100,97,98,96,107,105,106,103,104,102,679,697,698,694,563,562,561,558,559,560,553,554,552,556,557,555,294,295,296,297,298,299,292,293,291,288,289,290,618,619,620,621,622,623,616,617,615,612,613,614,228,229,230,231,232,233,234,235,236,237,238,239,186,187,188,189,190,191,184,185,183,180,181,182,663,664,674,671,415,414,416,417,418,419,412,413,411,408,409,410,359,357,358,355,356,354,350,348,349,353,351,352,530,528,529,533,531,532,536,534,535,539,537,538,209,207,208,205,206,204,215,213,214,211,212,210,470,468,469,473,471,472,476,474,475,479,477,478,680,691,696,695,136,135,137,134,132,133,141,142,143,140,138,139,601,602,600,604,605,603,607,608,606,610,611,609,548,546,547,551,549,550,543,544,545,542,540,541,218,216,217,221,219,220,224,222,223,227,225,226,287,285,286,283,284,282,278,276,277,281,279,280,667,681,690,686,370,369,371,368,366,367,360,361,362,363,364,365,25,26,24,28,29,27,31,32,30,34,35,33,489,490,491,488,486,487,480,481,482,483,484,485,423,424,425,422,420,421,429,430,431,428,426,427,151,152,150,154,155,153,149,147,148,145,146,144,692,699,702,701,509,508,507,504,505,506,514,515,513,510,511,512,446,444,445,449,447,448,452,450,451,455,453,454,52,53,51,48,49,50,58,59,57,54,55,56,392,390,391,395,393,394,387,388,389,386,384,385,90,91,92,93,94,95,88,89,87,84,85,86,662,665,676,670,575,574,573,570,571,572,565,566,564,568,569,567,625,626,624,628,629,627,631,632,630,634,635,633,114,115,116,117,118,119,112,113,111,108,109,110,241,242,240,244,245,243,247,248,246,250,251,249,73,74,72,76,77,75,79,80,78,82,83,81,666,677,687,682 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, M = {64} 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 15:54:01 · history