Equation 677 Database

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Magma badc31ba542a…

magma badc31ba542a
Size
381
Isomorphism class hash
badc31ba542af133e3b40eb591b90d47b4e8a00bbc8d38bd359db0634ceeb8a3
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 23:45:08
Display reorder
380,33,28,268,13,18,22,189,179,184,204,194,199,214,218,209,229,234,224,69,74,64,8,279,9,149,294,144,134,139,129,274,39,44,49,54,59,89,79,84,99,94,284,323,321,322,320,318,319,238,243,248,253,258,263,169,174,164,299,159,154,114,109,104,289,124,119,373,364,338,359,333,369,349,354,344,379,32,27,267,12,17,24,188,178,183,203,193,198,213,217,208,228,233,223,68,73,63,6,278,7,148,293,143,133,138,128,273,38,43,48,53,58,88,78,83,98,93,283,308,306,307,311,309,310,237,242,247,252,257,262,168,173,163,298,158,153,113,108,103,288,123,118,372,363,337,358,332,368,348,353,343,378,31,26,266,10,15,21,186,177,182,201,190,195,211,216,206,227,232,222,65,70,61,1,276,3,147,292,142,132,137,127,271,35,40,45,51,56,85,76,81,95,90,281,304,305,303,300,302,301,235,241,246,250,255,260,166,171,162,295,156,151,112,107,102,287,122,117,371,362,336,357,330,365,346,351,341,376,30,25,265,11,16,20,187,175,180,202,192,197,210,219,205,225,230,220,67,72,62,5,277,4,146,290,141,130,135,126,272,37,42,47,52,57,87,77,82,97,92,282,315,316,317,312,313,314,236,240,245,251,256,261,167,170,160,297,157,152,111,106,101,286,121,115,370,360,335,356,331,367,347,352,342,377,34,29,269,14,19,23,185,176,181,200,191,196,212,215,207,226,231,221,66,71,60,2,275,0,145,291,140,131,136,125,270,36,41,46,50,55,86,75,80,96,91,280,327,328,329,324,325,326,239,244,249,254,259,264,165,172,161,296,155,150,110,105,100,285,120,116,374,361,339,355,334,366,345,350,340,375 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#dba6afe67f86b36e533f777300b41b8ae8b2a840d4529c92a6cd7ab996e48d4f, M = {66} 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 23:45:09 · history