Equation 677 Database

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Magma 3f2e34cbcd8d…

magma 3f2e34cbcd8d
Size
381
Isomorphism class hash
3f2e34cbcd8d2e46f8bae59fcdfee510bcf6d3283de67423fd5768bf0f1dceac
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 23:46:31
Display reorder
380,123,122,124,125,120,121,229,234,239,214,219,224,129,130,131,126,127,128,310,305,306,307,308,309,204,209,184,189,194,199,114,115,116,117,118,119,294,249,254,264,274,284,143,138,139,140,141,142,175,176,177,178,179,174,259,269,279,289,299,244,136,134,137,132,133,135,374,353,354,355,337,368,336,378,335,364,98,97,99,100,101,96,227,232,237,212,217,222,77,72,73,74,75,76,318,319,320,321,322,317,202,207,182,187,192,197,93,94,95,90,91,92,292,247,252,262,272,282,86,87,88,89,84,85,169,170,171,172,173,168,258,268,278,288,298,243,83,81,78,79,80,82,370,350,338,333,351,366,339,375,359,361,38,37,39,40,41,36,228,233,238,213,218,223,17,12,13,14,15,16,315,316,311,312,313,314,203,208,183,188,193,198,33,34,35,30,31,32,293,248,253,263,273,283,26,27,28,29,24,25,9,10,11,6,7,8,256,266,276,286,296,241,23,21,18,19,20,22,373,344,334,330,345,367,343,376,341,363,148,147,149,144,145,146,226,230,235,211,216,221,151,152,153,154,155,150,329,301,302,303,304,300,200,205,181,186,190,195,167,162,163,164,165,166,291,246,251,261,271,281,157,158,159,160,161,156,110,111,112,113,108,109,257,267,277,287,297,242,5,3,1,0,2,4,372,356,357,332,340,369,358,377,342,362,64,63,65,60,61,62,225,231,236,210,215,220,67,68,69,70,71,66,324,325,326,327,328,323,201,206,180,185,191,196,47,42,43,44,45,46,290,245,250,260,270,280,54,55,56,57,58,59,103,104,105,106,107,102,255,265,275,285,295,240,49,53,50,51,52,48,371,331,348,346,347,365,349,379,352,360 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#dc50bff4268d4e886a12bccb100fd4b53117610e2c07e48d4c792db14c6c3b47, M = {74} 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 23:46:32 · history