Equation 677 Database

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Magma 631a10053fa3…

magma 631a10053fa3
Size
705
Isomorphism class hash
631a10053fa3749afceb23f68f5c932f66303b132c076c7659724cf4749a3db6
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 17:21:00
Display reorder
660,402,18,174,110,366,403,19,172,108,367,401,20,173,109,365,21,398,177,113,362,175,399,22,111,363,23,400,176,112,364,393,16,169,116,357,394,17,170,114,358,392,15,171,115,356,12,396,168,119,360,13,397,166,117,361,14,395,167,118,359,665,661,663,670,38,426,269,390,0,36,427,270,391,2,37,425,271,389,1,422,41,268,386,4,266,39,423,387,5,424,40,267,388,3,44,417,260,381,7,42,418,261,382,8,43,416,262,380,6,420,47,263,384,10,421,45,264,385,11,419,46,265,383,9,686,690,685,687,58,641,28,606,486,59,642,29,607,487,57,640,27,605,485,637,54,24,602,482,25,55,638,603,483,639,56,26,604,484,49,632,34,597,477,50,633,35,598,478,48,631,33,596,476,635,52,30,600,480,636,53,31,601,481,634,51,32,599,479,671,666,664,672,546,278,194,97,522,547,279,195,98,523,545,280,193,96,521,281,542,190,100,518,191,543,282,101,519,283,544,192,99,520,537,276,200,103,513,538,277,201,104,514,536,275,199,102,512,272,540,196,106,516,273,541,197,107,517,274,539,198,105,515,677,679,680,682,294,534,203,582,510,295,535,204,583,511,293,533,202,581,509,530,290,206,578,506,207,291,531,579,507,532,292,205,580,508,285,525,209,573,501,286,526,210,574,502,284,524,208,572,500,528,288,212,576,504,529,289,213,577,505,527,287,211,575,503,669,667,662,668,570,125,66,378,450,571,123,67,379,451,569,124,68,377,449,121,566,69,374,446,70,567,122,375,447,120,568,71,376,448,561,131,64,369,441,562,129,65,370,442,560,130,63,368,440,127,564,60,372,444,128,565,61,373,445,126,563,62,371,443,694,695,697,696,653,145,139,618,155,659,658,140,656,657,652,144,138,617,156,148,649,142,614,158,143,650,146,615,159,147,651,141,616,157,644,151,137,609,161,645,149,135,610,162,643,150,136,608,160,154,647,133,612,164,152,648,134,613,165,153,646,132,611,163,702,703,704,701,214,185,297,245,225,654,186,298,246,655,221,184,296,247,229,188,222,300,244,226,301,223,189,242,227,187,224,299,243,228,220,183,303,236,233,218,181,304,237,234,219,182,302,238,235,179,216,306,239,232,180,217,307,240,230,178,215,305,241,231,698,700,699,693,558,474,354,463,498,559,475,355,461,499,557,473,353,462,497,470,554,350,459,494,351,555,471,460,495,472,556,352,458,496,549,465,345,454,489,550,466,346,452,490,548,464,344,453,488,468,552,348,457,492,469,553,349,455,493,467,551,347,456,491,673,678,681,675,414,594,83,257,629,415,595,81,258,630,413,593,82,259,628,590,410,79,256,625,80,411,591,254,626,592,412,78,255,627,405,585,74,248,620,406,586,72,249,621,404,584,73,250,619,588,408,77,251,623,589,409,75,252,624,587,407,76,253,622,676,684,674,683,314,438,95,342,323,315,439,93,343,324,316,437,94,341,325,434,317,91,338,322,92,318,435,339,320,436,319,90,340,321,312,429,86,333,329,313,430,84,334,330,311,428,85,332,331,432,308,89,336,328,433,309,87,337,326,431,310,88,335,327,689,691,692,688 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#4f47b623d963c151ceba4da4fdb4170837133dc09cb743e53f258ef94ac4defc, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 17:21:01 · history