Equation 677 Database

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Magma e299324ea45b…

magma e299324ea45b
Size
381
Isomorphism class hash
e299324ea45bbdc70f0141e8a91c50d1e591b35a90916dd580077e6a08ddc4a0
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 23:16:18
Display reorder
380,329,328,327,325,326,324,127,132,137,142,147,292,61,50,56,70,66,276,191,196,201,175,180,185,11,1,6,21,16,267,150,155,296,162,165,170,107,287,102,122,112,117,40,271,45,25,32,36,241,246,235,255,260,250,221,231,205,215,210,226,82,77,282,92,97,87,330,352,341,371,362,357,366,335,345,376,323,322,321,319,320,318,125,130,135,141,145,290,63,51,57,72,68,278,193,198,203,178,183,188,10,0,5,20,15,266,151,156,295,161,166,171,105,286,100,121,110,115,41,270,46,26,31,37,240,245,236,256,261,251,223,233,208,218,213,228,81,76,280,91,95,86,331,350,340,373,360,356,368,336,349,378,300,301,302,303,304,305,126,131,136,140,146,291,62,52,58,73,67,277,192,197,202,177,182,187,13,3,8,23,19,268,152,157,297,160,167,172,106,285,101,120,111,116,42,272,47,27,33,38,243,248,238,258,263,253,222,232,207,217,212,227,80,75,281,90,96,85,333,351,342,372,361,355,365,337,346,377,309,311,310,308,306,307,128,133,138,143,148,293,60,53,55,71,65,275,190,195,200,176,181,186,12,2,7,22,17,265,153,158,298,163,168,173,108,288,103,123,113,118,43,273,48,28,30,35,242,247,237,257,262,252,220,230,206,216,211,225,83,78,283,93,98,88,332,353,343,370,363,358,367,338,347,375,314,313,312,316,317,315,129,134,139,144,149,294,64,54,59,74,69,279,194,199,204,179,184,189,14,4,9,24,18,269,154,159,299,164,169,174,109,289,104,124,114,119,44,274,49,29,34,39,244,249,239,259,264,254,224,234,209,219,214,229,84,79,284,94,99,89,334,354,344,374,364,359,369,339,348,379 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#056eca7eaa44680acb1d0f30609b5545e916e9d925bf21b77056bf3e64b490d0, 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 23:16:19 · history