Equation 677 Database

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Magma b91b01d872bb…

magma b91b01d872bb
Size
595
Isomorphism class hash
b91b01d872bb886dd5035ccef3b6d278db96e6be91ce79bab7be66c0d599361d
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
2026-10-06 22:27:36
Display reorder
381,380,382,383,378,379,507,506,508,509,505,504,455,454,450,451,452,453,411,410,412,413,408,409,271,272,270,274,275,273,555,576,577,594,593,371,366,367,368,369,370,373,372,374,375,376,377,441,440,442,443,438,439,499,498,500,501,502,503,277,281,276,278,279,280,328,327,329,324,325,326,483,482,484,485,480,481,52,51,50,47,48,49,132,131,133,135,136,134,255,257,256,254,252,253,191,190,192,194,195,193,56,58,57,53,54,55,99,98,100,96,97,95,46,45,44,41,42,43,63,62,64,59,60,61,225,227,226,222,223,224,541,530,511,516,535,525,548,550,521,560,571,567,562,578,589,584,473,468,469,470,471,472,356,355,357,358,359,354,430,429,431,426,427,428,462,467,463,464,465,466,493,492,494,495,496,497,435,434,436,437,432,433,487,486,488,489,490,491,151,150,149,152,153,154,21,23,22,18,19,20,236,235,234,238,239,237,199,201,200,196,197,198,160,159,161,156,158,157,17,16,15,14,12,13,4,3,5,2,1,0,11,10,9,7,8,6,219,221,220,216,217,218,540,532,510,515,537,526,546,551,522,556,572,566,561,579,588,583,393,394,395,390,391,392,419,418,414,415,416,417,385,384,386,387,388,389,407,406,402,403,404,405,284,283,285,286,287,282,315,314,316,317,312,313,449,448,444,445,446,447,87,86,88,85,83,84,164,162,163,167,165,166,248,247,246,250,251,249,208,181,180,183,209,182,115,114,113,118,116,117,76,75,74,73,71,72,81,80,82,79,77,78,104,106,105,103,101,102,264,266,265,267,268,269,542,531,512,519,539,527,547,552,524,559,573,568,563,580,590,585,344,345,346,347,342,343,337,336,338,339,340,341,304,303,305,300,301,302,334,333,335,330,331,332,290,289,291,292,293,288,306,311,307,308,309,310,458,457,459,460,461,456,91,90,89,92,93,94,69,68,70,66,67,65,210,211,212,213,214,215,207,206,205,204,202,203,179,178,177,176,174,175,130,129,128,127,125,126,142,141,140,137,138,139,31,30,29,33,34,32,241,240,242,244,245,243,543,534,513,518,538,529,545,553,523,558,574,570,565,581,591,586,361,362,363,364,365,360,401,400,396,397,398,399,323,322,318,319,320,321,474,479,475,476,477,478,351,350,352,353,348,349,425,424,420,421,422,423,296,295,297,298,299,294,122,124,123,120,121,119,108,107,109,111,112,110,263,262,261,259,260,258,185,184,186,188,189,187,173,172,171,170,169,168,143,145,144,146,147,148,155,27,28,26,24,25,37,36,35,39,40,38,232,231,233,229,230,228,544,533,514,517,536,528,549,554,520,557,575,569,564,582,592,587 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#33d45c5563bf4abb244f69cfa51749fb5a869f311e4fb00d8e6c25812252a226, M = the submagma generated by {0, 12} (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 2026-10-06 22:27:37 · history