Equation 677 Database

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Magma 04e61e9ac32b…

magma 04e61e9ac32b
Size
705
Isomorphism class hash
04e61e9ac32b9d10ed194cc969dd1e6abe9177f8c706884f1f91589084b09a7c
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 16:38:08
Display reorder
660,522,507,372,277,492,373,508,523,278,493,524,509,276,494,374,506,521,371,273,491,504,519,369,274,489,505,520,370,275,490,378,513,283,498,483,379,514,284,499,484,380,515,282,500,485,516,377,279,501,486,517,375,280,502,487,518,376,281,503,488,682,683,681,685,26,321,230,65,414,228,322,24,63,415,25,323,64,416,229,324,29,226,61,413,325,27,227,62,411,326,28,225,60,412,236,32,71,327,405,234,30,69,328,406,235,31,70,329,407,35,232,67,330,408,33,233,68,331,409,34,231,66,332,410,664,667,663,671,561,7,426,239,76,427,8,562,237,77,563,6,238,75,428,10,560,425,242,72,11,558,423,240,73,9,559,424,241,74,417,552,245,5,82,418,553,243,3,83,419,554,244,4,81,555,420,248,0,78,556,421,246,2,79,557,422,247,1,80,679,686,687,675,636,637,640,40,642,648,645,644,41,650,653,652,39,658,656,628,629,632,36,634,613,612,616,37,618,620,621,624,38,626,480,170,46,173,510,481,168,47,171,511,482,169,45,172,512,589,590,42,592,593,596,600,43,597,602,605,608,44,604,610,703,698,700,704,477,354,295,196,390,296,355,478,197,391,479,356,195,392,294,353,476,291,192,389,351,474,292,193,387,352,475,293,194,388,286,468,187,345,381,287,469,188,346,382,285,470,186,347,383,471,289,190,348,384,472,290,191,349,385,473,288,189,350,386,690,692,691,693,549,165,573,16,254,574,166,550,17,252,551,167,15,253,575,164,548,572,12,250,162,546,570,13,251,163,547,571,14,249,564,540,22,156,260,565,541,23,157,258,566,542,21,158,259,543,567,18,159,256,544,568,19,160,257,545,569,20,161,255,665,670,669,672,312,431,303,203,143,304,429,313,201,141,314,430,202,142,305,434,311,306,199,139,432,309,307,200,140,433,310,308,198,138,301,318,209,437,134,302,319,207,435,132,300,320,208,436,133,317,297,205,440,137,315,298,206,438,135,316,299,204,439,136,694,695,696,689,585,150,534,357,450,535,151,586,358,451,587,152,359,452,536,153,584,533,360,449,154,582,531,361,447,155,583,532,362,448,525,576,363,148,441,526,577,364,149,442,527,578,365,147,443,579,528,366,144,444,580,529,367,145,445,581,530,368,146,446,673,688,677,684,639,641,643,87,638,651,649,647,88,646,655,657,89,654,659,633,631,635,86,630,617,615,619,84,614,625,623,627,85,622,537,467,93,495,212,538,465,94,496,210,539,466,95,497,211,594,595,92,591,588,599,603,90,601,598,607,611,91,609,606,699,697,702,701,223,58,402,343,184,403,59,224,344,185,222,57,342,183,404,54,219,401,339,180,55,220,399,340,181,56,221,400,341,182,393,214,334,49,175,394,215,335,50,176,395,213,333,48,174,217,396,337,52,178,218,397,338,53,179,216,398,336,51,177,661,666,668,662,268,462,106,118,129,107,463,269,119,130,267,464,117,131,105,461,271,102,114,128,459,272,103,115,126,460,270,104,116,127,97,266,109,453,120,98,264,110,454,121,96,265,108,455,122,262,100,112,456,123,263,101,113,457,124,261,99,111,458,125,678,674,676,680 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#37e131d0061e11ac6a08c1b5043c4a4bd1e23715ce44e1796d2c3958c15ae4cf, 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 16:38:09 · history