Equation 677 Database

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Magma 13e060f93557…

magma 13e060f93557
Size
381
Isomorphism class hash
13e060f93557469f9ac876f14c9a999e3cb965fa2ff366f6639360cb3eb6ccbe
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:21:14
Display reorder
380,119,118,114,115,116,117,110,111,112,113,108,109,172,173,168,169,170,171,67,68,69,70,71,66,325,326,327,328,329,324,255,265,275,284,295,245,178,179,174,175,176,177,263,273,282,293,243,253,235,185,195,205,215,225,64,65,60,61,62,63,203,213,223,233,183,193,367,330,359,362,351,343,373,342,375,350,4,3,5,1,0,2,10,11,6,7,8,9,87,88,89,84,85,86,12,13,14,15,16,17,301,300,302,303,304,305,250,260,270,289,291,240,95,90,91,92,93,94,267,277,286,297,247,257,230,181,190,200,210,220,18,19,20,21,22,23,207,217,227,237,187,197,366,347,346,363,333,335,377,336,371,334,157,156,158,159,160,161,163,164,165,166,167,162,144,145,146,147,148,149,26,27,28,29,24,25,307,308,309,310,311,306,258,268,278,287,298,248,153,154,155,150,151,152,262,272,280,292,242,252,238,188,198,208,218,228,35,30,31,32,33,34,201,211,221,231,180,191,365,356,331,369,357,338,372,337,378,358,129,128,130,131,126,127,120,121,122,123,124,125,82,83,78,79,80,81,100,101,96,97,98,99,322,323,318,319,320,321,254,264,274,283,294,244,75,76,77,72,73,74,266,276,285,296,246,256,234,184,194,204,214,224,105,106,107,102,103,104,206,216,226,236,186,196,364,344,345,360,353,349,376,348,374,352,52,51,53,48,49,50,59,54,55,56,57,58,135,136,137,132,133,134,45,46,47,42,43,44,314,315,316,317,312,313,251,261,271,281,290,241,143,138,139,140,141,142,269,279,288,299,249,259,232,182,192,202,212,222,37,38,39,40,41,36,209,219,229,239,189,199,368,355,354,361,332,339,379,340,370,341 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#3136fd46544160d7110a12defb5eea5a4c1d4e69d8e8a4280fa062cfc3b165d6, M = {75} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:21:15 · history