Equation 677 Database

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Magma 102ea06f70bb…

magma 102ea06f70bb
Size
595
Isomorphism class hash
102ea06f70bb29ae322f778eb0dcb25b08f7b57810e35ddc082a8e4fe2f3651c
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
2026-10-07 22:09:53
Display reorder
164,166,165,163,161,162,120,122,121,119,117,118,79,78,80,75,76,77,409,408,410,411,412,413,388,387,389,384,385,386,522,536,529,563,567,140,139,138,141,142,143,133,132,134,131,129,130,146,145,144,147,148,170,156,155,157,158,159,160,191,187,195,183,256,253,239,238,240,241,242,243,246,245,244,247,248,249,105,107,106,109,110,108,364,363,365,360,361,362,331,330,332,333,334,335,416,415,417,418,419,414,314,313,315,316,317,312,281,280,276,277,278,279,407,406,402,403,404,405,265,264,266,267,268,269,272,271,273,274,275,270,537,527,550,535,533,543,531,551,579,573,574,565,555,572,559,568,213,212,211,214,215,216,227,226,228,231,229,230,250,254,180,193,185,189,83,82,81,85,86,84,89,88,87,90,91,92,98,97,96,94,95,93,31,30,32,35,33,34,206,205,207,210,208,209,490,489,491,486,487,488,426,431,427,428,429,430,368,367,369,370,371,366,460,459,461,456,457,458,300,305,301,302,303,304,287,286,282,283,284,285,424,423,425,420,421,422,382,381,383,378,379,380,540,552,525,523,545,524,548,513,592,584,554,569,586,577,588,561,53,52,51,54,55,56,151,150,149,152,153,154,102,104,103,100,101,99,27,29,28,26,24,25,2,0,1,3,4,5,20,19,18,22,23,21,12,14,13,16,17,15,123,125,124,127,128,126,309,308,310,311,306,307,496,495,497,492,493,494,485,484,480,481,482,483,399,398,400,401,396,397,509,508,504,505,506,507,377,376,372,373,374,375,432,437,433,434,435,436,329,328,324,325,326,327,526,530,511,512,517,519,534,510,594,558,591,576,571,560,566,583,197,196,198,223,224,225,201,200,199,202,203,204,252,257,181,194,186,190,43,42,44,39,40,41,11,10,9,6,7,8,60,62,61,59,57,58,70,69,71,74,72,73,172,171,173,168,169,167,471,470,472,473,468,469,445,444,446,447,448,449,466,465,467,462,463,464,356,355,357,358,359,354,440,439,441,442,443,438,292,291,293,288,289,290,295,294,296,297,298,299,452,451,453,454,455,450,541,538,518,515,547,514,544,521,593,578,562,580,556,585,570,575,115,114,116,113,111,112,38,37,36,135,136,137,46,45,47,50,48,49,175,174,176,177,178,179,188,184,192,182,255,251,235,237,236,234,232,233,220,222,221,218,219,217,68,67,66,63,64,65,395,394,390,391,392,393,476,475,477,478,479,474,502,501,503,498,499,500,339,338,340,341,336,337,263,262,259,258,260,261,352,351,353,348,349,350,321,320,322,323,318,319,345,344,346,347,342,343,516,520,549,539,528,542,532,546,553,564,581,582,587,589,557,590 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#f04ca8125d7ce546c7552606527b36663a07f654279810fba8dfdb3271b338ee, M = the submagma generated by {0, 36} (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 2026-10-07 22:09:54 · history