Equation 677 Database

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Magma 272a83f02fca…

magma 272a83f02fca
Size
381
Isomorphism class hash
272a83f02fca2a011d75835d5a9fa0ae5c7f9ee1e874b1ce3a51cde99ee9080a
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 23:15:40
Display reorder
380,138,148,143,163,153,158,133,123,128,118,108,113,281,286,275,265,270,260,256,245,250,241,231,236,220,210,215,205,195,200,58,293,63,68,73,78,8,9,7,5,6,225,173,178,168,188,193,183,324,325,326,327,328,329,38,30,50,46,41,25,103,299,98,88,93,83,343,358,368,373,335,353,330,378,345,361,137,147,142,162,152,157,132,122,127,117,107,112,282,287,277,266,271,261,255,246,251,240,230,235,222,212,216,206,196,202,57,292,62,67,72,77,12,13,14,10,11,226,172,177,167,187,192,182,321,322,323,318,319,320,37,31,51,45,40,27,102,297,97,87,92,82,342,357,367,372,336,352,331,377,347,360,139,149,144,164,154,159,134,124,129,119,109,114,284,289,279,269,274,264,259,249,254,244,234,239,223,213,218,209,198,203,59,294,64,69,74,79,1,0,2,3,4,229,174,179,169,189,194,184,315,316,317,312,313,314,35,32,52,47,42,28,104,298,99,89,94,84,344,359,369,374,339,354,332,379,349,364,136,145,141,160,150,155,131,121,126,116,106,111,280,285,276,267,272,262,257,247,252,242,232,237,224,214,219,208,199,204,55,291,60,66,71,76,19,15,16,17,18,227,170,175,166,186,191,181,309,310,311,306,307,308,39,33,54,48,44,29,100,296,95,85,90,80,341,356,366,371,337,351,333,375,346,362,135,146,140,161,151,156,130,120,125,115,105,110,283,288,278,268,273,263,258,248,253,243,233,238,221,211,217,207,197,201,56,290,61,65,70,75,23,21,22,20,24,228,171,176,165,185,190,180,301,300,302,303,304,305,36,34,53,49,43,26,101,295,96,86,91,81,340,355,365,370,338,350,334,376,348,363 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 = {66} 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 23:15:41 · history