Equation 677 Database

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Magma 8571a7ebab7c…

magma 8571a7ebab7c
Size
595
Isomorphism class hash
8571a7ebab7c44d2dcc27cfc1c362d1f0ae90a6ca580696ec64cf4e44fb797fe
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 00:26:51
Display reorder
99,98,100,101,96,97,53,52,48,49,50,51,324,326,325,327,328,329,386,385,384,381,382,383,357,359,358,362,360,361,511,513,510,564,574,308,310,309,306,307,311,40,39,41,36,37,38,30,35,31,32,33,34,243,242,244,245,240,241,224,223,225,226,227,222,103,102,104,105,106,107,144,149,145,146,147,148,70,66,69,67,68,71,166,165,167,162,163,164,131,130,126,127,128,129,312,314,313,316,317,315,395,394,393,397,398,396,404,403,402,400,401,399,347,346,345,343,344,342,485,483,509,508,482,484,406,467,432,466,431,465,529,530,525,527,533,528,583,578,550,594,545,558,543,555,561,554,188,190,189,186,187,191,17,16,12,13,14,15,170,169,171,172,173,168,182,181,183,184,185,180,275,274,270,271,272,273,238,237,239,234,235,236,141,140,142,143,138,139,220,216,219,217,218,221,254,253,255,256,257,252,117,116,118,119,114,115,452,453,418,492,501,491,489,499,490,488,486,487,507,479,500,480,439,440,481,445,444,442,443,441,356,355,354,351,352,353,407,470,434,468,433,469,541,524,512,539,540,522,563,588,582,566,577,557,565,553,585,562,8,10,9,6,7,11,233,232,228,229,230,231,2,0,3,4,5,1,297,296,298,299,294,295,177,176,178,179,174,175,55,54,56,57,58,59,264,269,265,266,267,268,120,122,125,123,124,121,214,213,215,210,211,212,262,261,263,258,259,260,336,338,337,340,341,339,415,417,416,414,413,412,322,321,323,318,319,320,333,335,334,332,330,331,478,477,506,411,505,476,473,409,472,504,471,408,535,536,523,521,520,519,592,573,572,580,575,587,581,586,576,579,76,72,77,74,75,73,135,134,136,137,132,133,87,86,88,89,84,85,81,80,82,83,78,79,207,206,208,209,204,205,202,201,203,198,199,200,248,247,249,250,251,246,44,46,43,47,42,45,93,92,94,95,90,91,284,283,285,286,287,282,460,424,423,348,349,350,390,392,391,389,387,388,372,374,373,371,370,427,426,462,369,461,425,435,367,366,368,365,363,364,422,420,502,498,503,421,532,542,514,534,518,515,547,571,569,546,544,584,556,590,549,548,64,60,65,62,63,61,278,277,279,280,281,276,302,301,303,304,305,300,109,108,110,111,112,113,20,19,21,22,23,18,288,293,289,290,291,292,27,26,28,29,24,25,157,159,156,160,161,158,192,197,193,194,195,196,152,151,153,154,155,150,494,457,456,454,455,493,474,437,436,410,438,475,449,451,450,448,446,447,428,463,405,464,429,430,377,376,375,378,379,380,419,496,458,497,459,495,537,538,531,526,516,517,552,551,591,559,560,570,589,567,568,593 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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, 5, B) with E = magma#10d95f4d62da29d597cabb26c5d7a2889acb76e08f2897cdd164594c6bfbc5c4, M = the submagma generated by {36, 42} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-08 00:26:52 · history