Equation 677 Database

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Magma f8f74eb43d73…

magma f8f74eb43d73
Size
381
Isomorphism class hash
f8f74eb43d73026c940da2cab00b57480f8fa415a34598c5698e21c2e013af7d
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 23:23:18
Display reorder
380,110,115,291,105,96,100,126,131,121,140,146,135,257,246,251,275,261,265,75,84,70,281,90,85,295,25,26,24,22,23,322,323,321,319,320,318,165,171,176,150,156,161,222,226,217,235,285,230,1,0,241,33,3,2,15,16,17,271,14,210,206,201,196,185,190,180,350,345,355,361,368,335,331,376,341,370,113,118,293,108,98,103,128,133,123,143,148,138,258,248,253,278,263,268,78,82,73,283,93,88,298,10,9,7,8,6,324,325,326,327,328,329,168,173,178,153,158,163,223,228,218,238,288,233,5,4,243,11,12,13,54,52,53,273,55,213,208,203,198,188,193,183,353,348,358,362,367,338,333,378,343,373,111,116,290,106,95,101,125,130,120,141,145,136,256,247,252,276,260,266,76,80,71,280,91,86,296,27,18,20,21,19,306,307,308,309,310,311,167,172,177,152,157,162,220,225,215,236,286,231,31,32,240,28,29,30,45,44,47,270,46,211,207,202,197,187,192,182,351,346,356,360,365,336,332,375,340,371,112,117,292,107,97,102,127,132,122,142,147,137,255,245,250,277,262,267,77,81,72,282,92,87,297,36,37,38,34,35,316,317,315,313,314,312,166,170,175,151,155,160,221,227,216,237,287,232,43,42,242,41,39,40,50,48,49,272,51,212,205,200,195,186,191,181,352,347,357,364,366,337,330,377,342,372,114,119,294,109,99,104,129,134,124,144,149,139,259,249,254,279,264,269,79,83,74,284,94,89,299,63,64,62,60,61,301,300,302,303,304,305,169,174,179,154,159,164,224,229,219,239,289,234,68,69,244,66,67,65,58,56,57,274,59,214,209,204,199,189,194,184,354,349,359,363,369,339,334,379,344,374 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 = {75} 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 23:23:19 · history