Equation 677 Database

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Magma 7cc7672da5d8…

magma 7cc7672da5d8
Size
381
Isomorphism class hash
7cc7672da5d84bd0c39ad347a862f5f78026e4fc5f53349de1ff1b60069bbf76
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 23:21:10
Display reorder
380,124,123,125,120,121,122,291,240,250,260,279,281,87,88,89,84,85,86,285,295,245,255,265,274,201,211,221,231,180,191,313,314,315,316,317,312,215,225,235,185,195,205,90,91,92,93,94,95,175,176,177,178,179,174,131,126,127,128,129,130,168,169,170,171,172,173,359,346,361,358,373,371,345,332,364,351,112,111,113,108,109,110,294,244,254,264,273,284,96,97,98,99,100,101,280,292,242,252,262,270,204,214,224,234,184,194,308,309,310,311,306,307,210,220,230,181,190,200,107,102,103,104,105,106,143,138,139,140,141,142,119,114,115,116,117,118,136,137,132,133,134,135,352,348,365,353,375,372,347,349,360,350,152,151,153,154,155,150,293,243,253,263,272,283,76,77,72,73,74,75,289,299,249,259,269,278,203,213,223,233,183,193,318,319,320,321,322,323,219,229,239,189,199,209,82,83,78,79,80,81,67,68,69,70,71,66,146,147,148,149,144,145,60,61,62,63,64,65,342,344,368,341,374,379,343,355,362,354,4,3,5,1,0,2,297,247,257,267,276,287,44,45,46,47,42,43,282,290,241,251,261,271,207,217,227,237,187,197,302,303,304,305,301,300,212,222,232,182,192,202,40,41,36,37,38,39,24,25,26,27,28,29,11,6,7,8,9,10,30,31,32,33,34,35,335,337,367,336,377,370,338,331,369,330,156,161,157,158,159,160,296,246,256,266,275,286,16,17,12,13,14,15,288,298,248,258,268,277,206,216,226,236,186,196,327,328,329,324,325,326,218,228,238,188,198,208,22,23,18,19,20,21,51,52,53,48,49,50,163,164,165,166,167,162,58,59,54,55,56,57,339,334,366,340,376,378,333,356,363,357 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#3136fd46544160d7110a12defb5eea5a4c1d4e69d8e8a4280fa062cfc3b165d6, 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 23:21:11 · history