Equation 677 Database

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Magma 2530434ba20d…

magma 2530434ba20d
Size
381
Isomorphism class hash
2530434ba20d5599949eddd48b20b6b7338fd4d5caf5eb295f9173f27d78c50c
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 23:48:06
Display reorder
380,81,76,220,91,97,86,245,295,240,231,236,226,287,272,277,266,257,262,132,136,125,146,151,141,120,115,291,114,101,106,315,316,317,312,313,314,203,208,213,188,193,198,250,13,14,12,10,11,181,171,176,165,155,160,20,19,18,22,280,21,52,217,57,61,67,72,335,333,345,361,367,340,355,351,375,373,83,78,223,90,96,88,248,298,243,233,238,228,288,273,278,268,258,263,133,138,128,148,153,143,123,118,293,112,103,108,310,306,308,304,300,302,204,209,214,189,194,199,253,39,40,41,1,0,183,173,178,168,158,163,35,34,36,37,283,38,53,218,58,63,68,73,337,334,348,363,368,343,358,353,378,372,82,77,222,93,98,87,247,297,242,232,237,227,285,271,275,267,259,264,131,137,127,145,150,142,121,116,290,110,100,105,309,311,307,303,305,301,201,206,211,185,190,195,252,33,32,30,31,29,180,170,175,166,156,161,26,25,24,28,282,27,51,216,55,62,66,71,336,331,347,360,366,342,357,350,377,371,80,75,221,92,95,85,246,296,241,230,235,225,286,270,276,265,256,261,130,135,126,147,152,140,122,117,292,111,102,107,321,322,323,318,319,320,202,207,212,187,192,197,251,9,8,15,7,6,182,172,177,167,157,162,3,5,4,2,281,23,50,215,56,60,65,70,339,332,346,362,365,341,356,352,376,370,84,79,224,94,99,89,249,299,244,234,239,229,289,274,279,269,255,260,134,139,129,149,154,144,124,119,294,113,104,109,326,324,325,329,327,328,200,205,210,186,191,196,254,47,48,49,16,17,184,174,179,169,159,164,43,42,44,45,284,46,54,219,59,64,69,74,338,330,349,364,369,344,359,354,379,374 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#e6667989dcd92e07f9ac29d8b243d6a96a38fa8a609415f393f811e1aaa26c76, M = {71} 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 23:48:07 · history