Equation 677 Database

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Magma 4a6e85afd1c3…

magma 4a6e85afd1c3
Size
381
Isomorphism class hash
4a6e85afd1c3dc8ba51233dd0e547d777d78333661c7bc20bd6379931ec2824d
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 23:22:57
Display reorder
380,273,288,278,268,258,263,128,133,122,143,148,138,307,308,306,310,311,309,283,75,223,74,72,73,155,160,150,170,175,165,33,215,32,30,31,29,233,238,228,248,298,243,191,180,186,205,195,200,112,292,117,97,103,109,79,253,80,76,77,78,19,21,20,23,22,211,367,330,360,358,377,336,352,348,340,372,272,286,276,265,256,261,126,131,121,140,145,135,319,320,318,322,323,321,281,51,220,50,48,49,156,162,152,172,176,166,47,217,46,44,45,43,231,236,226,245,295,240,192,182,187,207,197,202,110,291,115,95,101,107,14,251,13,11,12,10,39,38,40,41,42,212,366,332,362,355,376,337,350,345,342,370,270,285,275,267,257,262,127,132,124,142,147,137,325,326,324,328,329,327,282,65,222,64,63,66,159,164,154,174,179,169,62,218,61,59,60,58,232,237,227,247,297,242,194,184,189,209,199,204,114,294,119,99,100,105,71,252,70,69,67,68,54,53,55,56,57,213,369,334,363,357,379,338,354,347,343,374,271,287,277,266,255,260,125,130,120,141,146,136,315,316,317,312,313,314,280,52,221,35,36,37,157,161,151,171,177,167,17,216,18,15,16,34,230,235,225,246,296,241,190,181,185,206,196,201,111,290,116,96,102,106,3,250,4,1,0,2,25,24,26,27,28,210,365,331,361,356,375,335,351,346,341,371,274,289,279,269,259,264,129,134,123,144,149,139,302,301,300,305,303,304,284,94,224,93,91,92,158,163,153,173,178,168,90,219,89,87,88,86,234,239,229,249,299,244,193,183,188,208,198,203,113,293,118,98,104,108,8,254,9,5,6,7,82,81,83,84,85,214,368,333,364,359,378,339,353,349,344,373 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#45ae9dee612792667330602ba505951dcde187c4c1909cf40fbaf15f74e8af60, M = {70} 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 23:22:58 · history