Equation 677 Database

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Magma 1ba32fd4d1a8…

magma 1ba32fd4d1a8
Size
381
Isomorphism class hash
1ba32fd4d1a824baac154afef4d942fc34dea98431dd9d510b9f4282ec0df3f7
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 23:16:05
Display reorder
380,120,131,125,116,108,111,192,182,187,177,167,172,236,225,231,251,240,246,265,256,261,281,270,276,100,95,296,91,84,85,153,158,162,137,142,148,300,302,301,304,305,303,41,46,50,29,31,35,196,200,205,212,217,222,69,79,59,64,294,74,19,287,22,12,1,6,332,337,369,354,355,375,343,373,362,347,124,134,129,119,107,114,191,180,185,176,166,171,235,226,230,250,241,245,266,255,260,280,271,275,104,98,299,94,83,89,152,157,163,136,143,147,322,323,321,319,320,318,44,49,54,28,34,39,195,201,206,211,216,221,68,78,58,63,293,73,16,285,20,10,0,5,331,335,368,353,359,376,342,372,360,345,122,132,127,117,109,112,193,183,188,178,168,173,238,228,233,253,243,248,268,258,263,283,273,278,102,99,297,90,80,87,154,159,164,138,144,149,317,315,316,314,312,313,42,48,52,25,32,38,198,203,208,213,218,223,65,75,55,61,291,70,17,288,23,13,3,8,333,338,365,351,357,378,344,374,363,348,121,130,126,115,106,110,194,184,189,179,169,174,239,229,234,254,244,249,269,259,264,284,274,279,101,96,295,92,81,86,150,155,160,135,141,146,308,306,307,311,309,310,43,47,53,26,33,37,199,204,209,214,219,224,66,76,56,60,290,71,18,289,24,14,4,9,334,339,366,350,358,379,340,370,364,349,123,133,128,118,105,113,190,181,186,175,165,170,237,227,232,252,242,247,267,257,262,282,272,277,103,97,298,93,82,88,151,156,161,139,140,145,326,324,325,329,327,328,40,45,51,27,30,36,197,202,207,210,215,220,67,77,57,62,292,72,15,286,21,11,2,7,330,336,367,352,356,377,341,371,361,346 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#056eca7eaa44680acb1d0f30609b5545e916e9d925bf21b77056bf3e64b490d0, 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 23:16:06 · history