Equation 677 Database

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Magma 41ab7729f7a4…

magma 41ab7729f7a4
Size
399
Isomorphism class hash
41ab7729f7a4dbfd209836b1dfc7f123ee9f5b068ecf2bdd53313e07d1f0459c
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 11:34:26
Display reorder
48,49,50,51,52,53,45,46,47,41,42,43,44,36,37,38,39,40,381,327,305,13,323,14,328,297,315,15,329,298,316,330,16,299,317,17,331,300,318,9,332,301,319,324,10,302,320,325,11,303,321,326,12,304,322,289,336,6,307,290,337,7,308,291,338,8,309,292,339,1,310,293,340,0,311,294,341,2,312,295,333,3,313,296,334,4,314,288,335,5,306,391,385,386,392,205,105,285,78,286,206,106,79,287,198,107,80,199,279,99,72,280,200,100,73,281,201,101,74,202,282,102,75,203,283,103,76,204,284,104,77,98,214,278,87,90,215,270,88,91,207,271,89,92,208,272,81,93,209,273,82,94,210,274,83,95,211,275,84,96,212,276,85,97,213,277,86,383,389,390,384,123,217,161,56,153,124,218,57,154,125,219,58,117,155,220,59,156,118,221,60,157,119,222,61,120,158,223,62,121,159,224,54,122,160,216,55,226,116,145,65,227,108,146,66,228,109,147,67,229,110,148,68,230,111,149,69,231,112,150,70,232,113,151,71,233,114,152,63,225,115,144,64,388,398,397,387,349,265,189,343,190,351,266,345,191,353,267,346,355,192,268,348,193,357,269,350,194,359,261,352,342,195,262,354,344,196,263,356,347,197,264,358,258,367,182,361,259,369,183,363,260,371,184,365,252,373,185,366,253,375,186,368,254,377,187,370,255,360,188,372,256,362,180,374,257,364,181,376,394,395,396,393,176,141,240,34,241,177,142,35,242,178,143,27,179,234,135,28,235,171,136,29,236,172,137,30,173,237,138,31,174,238,139,32,175,239,140,33,134,169,249,18,126,170,250,19,127,162,251,20,128,163,243,21,129,164,244,22,130,165,245,23,131,166,246,24,132,167,247,25,133,168,248,26,379,380,378,382 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#262be896699ea81022bd129e5d1a465be934f78d54a1a8517aa405666e74c988, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 21.

last edited by qawbecrdtey at 2026-10-07 11:34:27 · history