Equation 677 Database

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Magma 290514f1cc4a…

magma 290514f1cc4a
Size
381
Isomorphism class hash
290514f1cc4a7797fda6737c63400bd8c6ab91f47db7083b26a2a34dcfd83d08
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 23:26:40
Display reorder
380,58,287,59,242,257,272,200,205,210,215,221,226,72,73,74,75,76,77,250,260,275,290,160,165,196,170,175,180,185,191,68,69,70,71,66,67,321,322,323,318,319,320,295,231,236,245,265,280,56,57,52,53,54,55,60,61,62,63,64,65,141,136,146,150,155,131,349,331,357,335,332,368,353,375,360,373,90,288,91,243,258,273,203,208,214,219,224,228,81,82,83,78,79,80,253,264,278,293,163,168,198,173,178,184,189,193,99,100,101,102,103,98,316,317,312,313,314,315,299,234,239,248,268,284,89,84,85,86,87,88,94,95,96,97,92,93,144,139,149,153,158,134,345,333,358,330,337,369,354,379,364,374,129,289,128,244,259,274,202,207,212,217,222,227,121,116,117,118,119,120,252,262,277,292,162,167,197,172,177,182,187,192,115,110,111,112,113,114,302,303,304,305,301,300,297,232,237,247,267,282,123,124,125,126,127,122,108,109,104,105,106,107,142,137,147,152,157,132,347,334,356,344,343,365,351,377,362,371,48,285,49,240,255,270,204,209,213,218,223,229,38,39,40,41,36,37,254,263,279,294,164,169,199,174,179,183,188,194,30,31,32,33,34,35,328,329,324,325,326,327,298,233,238,249,269,283,46,47,42,43,44,45,27,28,29,24,25,26,143,138,148,154,159,133,346,340,359,342,341,366,350,378,363,372,50,286,51,241,256,271,201,206,211,216,220,225,19,20,21,22,23,18,251,261,276,291,161,166,195,171,176,181,186,190,11,6,7,8,9,10,307,308,309,310,311,306,296,230,235,246,266,281,1,0,2,3,4,5,15,16,17,12,13,14,140,135,145,151,156,130,348,336,355,338,339,367,352,376,361,370 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#51f9fa4941789fcec91b298b71630f6443ab313fec0bf96b206088496fe3251b, M = {69} 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 23:26:41 · history