Equation 677 Database

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Magma 1fc0e88aaf8c…

magma 1fc0e88aaf8c
Size
381
Isomorphism class hash
1fc0e88aaf8c17eba1cc85be45839fc3f093dfec5d4149d3b105972a4a8d38a5
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 23:30:31
Display reorder
380,155,305,173,169,151,160,174,164,156,178,303,153,171,170,152,161,175,162,157,179,177,154,304,172,168,150,159,176,163,158,302,126,144,143,125,134,148,135,130,121,122,127,301,145,141,123,132,149,136,131,120,128,300,146,142,124,133,147,137,129,138,139,166,167,165,140,344,333,359,374,331,369,368,375,370,332,97,322,115,111,93,102,119,106,101,92,320,98,116,112,94,103,117,107,99,90,91,96,321,114,113,95,104,118,105,100,319,71,89,85,67,76,62,80,72,63,64,69,317,87,86,68,77,60,78,73,65,70,318,88,84,66,75,61,79,74,83,81,108,109,110,82,346,345,360,362,364,361,335,363,376,378,53,329,40,36,49,58,44,31,54,45,312,51,41,37,50,59,42,32,55,46,47,52,313,39,38,48,57,43,30,56,316,24,14,10,23,0,15,5,28,19,20,25,314,12,11,21,2,16,3,29,18,26,315,13,9,22,1,17,4,27,8,6,33,34,35,7,334,350,349,377,365,372,348,347,379,371,292,325,267,263,285,243,274,251,299,281,323,293,268,261,286,244,275,246,297,279,280,291,324,269,262,287,245,273,247,298,328,289,266,258,284,240,271,248,294,276,277,290,326,264,259,282,242,272,249,295,278,288,327,265,260,283,241,270,250,296,253,252,257,255,256,254,343,330,358,367,373,342,356,355,366,357,185,307,224,199,181,190,229,194,186,234,308,183,222,200,182,191,230,192,187,235,236,184,306,223,198,180,189,228,193,188,310,205,226,219,201,210,232,214,209,239,237,206,311,227,220,202,211,233,215,207,238,204,309,225,221,203,212,231,213,208,217,218,196,197,195,216,353,337,351,352,354,338,341,340,339,336 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#6c0663526a98218824273cacd03aac8d37a819b5d14a330cc1cd23f8e7fff8ad, 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 23:30:32 · history