Equation 677 Database

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Magma 77afdf1c67bd…

magma 77afdf1c67bd
Size
381
Isomorphism class hash
77afdf1c67bdad29a391b177162e5eee7c0fa596f9b6e3fbf792d42ea8ed8ade
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 23:39:10
Display reorder
380,125,120,130,136,141,146,267,277,262,250,255,247,16,295,15,13,14,12,304,305,303,300,302,301,101,105,96,291,115,110,27,211,270,24,25,26,76,280,71,92,84,85,285,230,235,226,215,220,23,1,241,2,3,0,160,150,155,176,166,171,200,196,205,180,185,190,345,351,355,367,340,361,330,336,376,371,127,122,132,137,142,147,266,276,260,251,256,245,11,296,10,9,17,8,313,314,312,316,317,315,102,107,97,292,117,112,4,210,271,7,5,6,77,282,72,90,81,87,286,231,236,225,216,221,21,22,240,18,19,20,162,152,157,177,167,172,202,197,207,182,187,192,346,352,356,365,342,362,332,335,375,372,129,124,134,139,144,149,269,279,264,254,259,249,64,299,63,61,62,60,328,329,327,325,326,324,104,109,99,294,119,114,59,214,274,56,57,58,79,284,74,94,83,89,289,234,239,229,219,224,69,68,244,67,65,66,164,154,159,179,169,174,204,199,209,184,189,194,349,354,359,369,343,364,334,339,379,374,126,121,131,135,140,145,265,275,261,252,257,246,36,297,35,33,34,32,311,309,310,308,306,307,100,106,95,290,116,111,31,212,272,28,29,30,75,281,70,91,80,86,287,232,237,227,217,222,41,40,242,39,37,38,161,151,156,175,165,170,201,195,206,181,186,191,347,350,357,366,341,360,331,337,377,370,128,123,133,138,143,148,268,278,263,253,258,248,50,298,49,47,48,46,318,319,320,321,322,323,103,108,98,293,118,113,45,213,273,42,43,44,78,283,73,93,82,88,288,233,238,228,218,223,55,54,243,53,51,52,163,153,158,178,168,173,203,198,208,183,188,193,348,353,358,368,344,363,333,338,378,373 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#a6a871b690da3ca50898b154241f95e49e76adc5851f18be5057763f1765447f, 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 23:39:11 · history