Equation 677 Database

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Magma 90a9143d49a7…

magma 90a9143d49a7
Size
381
Isomorphism class hash
90a9143d49a7df3156e7b870e6419d38d3be69d1ebe4b7ec2dccf211270e1820
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 23:49:43
Display reorder
380,133,128,138,143,293,148,198,203,193,183,188,178,118,123,113,7,288,6,314,312,313,317,315,316,77,82,72,67,277,62,267,12,17,24,27,30,252,257,262,238,242,248,37,42,47,52,57,272,108,103,283,98,88,93,298,168,173,153,158,163,223,233,228,218,209,214,347,368,358,372,332,337,353,342,363,377,130,125,135,141,290,145,196,202,192,182,186,176,116,121,111,0,286,1,301,300,302,303,304,305,78,83,73,68,278,63,268,13,18,21,28,33,253,258,263,235,243,246,38,43,48,53,58,273,105,100,281,95,85,90,296,165,170,151,156,161,221,231,227,217,208,212,348,366,356,373,333,338,351,343,360,376,131,126,136,140,291,146,195,200,190,180,185,175,115,120,110,3,285,2,326,324,325,329,327,328,76,80,71,66,275,61,266,10,16,20,25,31,251,256,261,236,241,245,36,41,45,50,55,270,106,101,280,96,86,91,295,166,171,150,155,160,220,230,225,215,207,211,345,365,355,370,331,336,350,340,361,375,132,127,137,142,292,147,197,201,191,181,187,177,117,122,112,5,287,4,319,320,318,322,323,321,75,81,70,65,276,60,265,11,15,22,26,32,250,255,260,237,240,247,35,40,46,51,56,271,107,102,282,97,87,92,297,167,172,152,157,162,222,232,226,216,205,213,346,367,357,371,330,335,352,341,362,379,134,129,139,144,294,149,199,204,194,184,189,179,119,124,114,8,289,9,311,309,310,308,306,307,79,84,74,69,279,64,269,14,19,23,29,34,254,259,264,239,244,249,39,44,49,54,59,274,109,104,284,99,89,94,299,169,174,154,159,164,224,234,229,219,206,210,349,369,359,374,334,339,354,344,364,378 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#edf00a573dad398077d9e9a7f74ac5f2ae5601c41b127cdfd29539dca9f6b98a, M = {70} 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 23:49:44 · history