Equation 677 Database

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Magma a54328e3e813…

magma a54328e3e813
Size
381
Isomorphism class hash
a54328e3e813da5ab6f7540eb4dd290638ac1f0d3e1c68427e63f06b58877d49
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 23:26:28
Display reorder
380,121,120,122,117,118,119,280,285,290,295,270,275,147,148,115,116,143,145,130,131,132,133,134,135,176,150,155,160,166,171,139,140,141,136,137,138,190,195,201,206,180,185,321,322,323,318,319,320,210,215,220,225,230,235,265,240,245,250,255,260,128,127,123,124,125,126,354,353,352,371,367,336,351,376,361,357,110,109,105,106,107,108,284,289,294,299,274,279,4,5,6,7,2,3,112,114,97,98,1,0,178,153,159,163,168,173,99,100,101,102,103,104,194,198,204,209,184,189,329,324,325,326,327,328,214,219,224,229,234,239,269,244,249,254,259,264,9,8,10,11,12,13,340,343,342,374,366,350,341,379,364,358,144,142,146,149,129,68,281,286,291,296,271,276,50,51,52,53,54,55,59,60,61,56,57,58,177,152,157,162,167,172,64,65,66,67,62,63,192,197,202,207,182,187,316,317,312,313,314,315,212,217,222,227,232,237,267,241,246,251,256,261,48,47,49,44,45,46,338,333,347,370,365,330,346,375,360,355,72,71,73,74,69,70,283,288,293,298,273,278,85,86,81,82,83,84,91,92,87,88,89,90,179,154,158,164,169,174,96,93,111,113,94,95,193,199,203,208,183,188,308,309,310,311,306,307,213,218,223,228,233,238,268,243,248,253,258,263,76,75,77,78,79,80,337,349,348,373,369,332,331,378,363,359,29,28,30,31,26,27,282,287,292,297,272,277,42,43,38,39,40,41,15,16,17,18,19,14,175,151,156,161,165,170,21,22,23,24,25,20,191,196,200,205,181,186,304,305,301,300,302,303,211,216,221,226,231,236,266,242,247,252,257,262,33,32,34,35,36,37,345,335,339,372,368,344,334,377,362,356 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 = {76} 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 23:26:29 · history