Equation 677 Database

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Magma 2d4936c05bea…

magma 2d4936c05bea
Size
381
Isomorphism class hash
2d4936c05bea10c4949167083fe7d94c63ed3e166d43c96c1da8a76cc5673b94
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 331 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:50:12
Display reorder
380,288,131,318,123,274,289,124,129,319,272,125,130,287,273,303,126,290,120,304,276,291,127,121,317,277,292,128,122,275,327,280,147,297,139,284,278,148,298,140,285,279,149,296,138,286,281,146,151,142,294,282,144,150,143,295,283,145,299,141,293,136,132,135,133,134,137,361,336,364,335,363,362,360,339,338,337,199,36,320,50,203,197,48,37,321,204,49,38,198,205,328,34,183,52,305,190,184,35,53,306,188,182,33,51,189,307,191,31,187,42,209,192,32,185,43,210,193,30,186,44,211,196,47,207,58,200,194,45,208,59,201,195,46,206,57,202,55,56,41,39,40,54,379,354,377,353,376,375,378,352,351,350,175,15,315,29,179,173,27,16,316,180,28,17,174,181,302,13,159,2,300,166,160,14,1,301,164,158,12,0,165,314,167,10,163,21,156,168,11,161,22,157,169,9,162,23,155,172,26,154,8,176,170,24,152,6,177,171,25,153,7,178,5,3,20,18,19,4,374,349,372,348,371,370,373,347,346,345,269,109,323,91,247,270,92,110,309,245,90,108,271,246,322,107,256,93,308,260,254,105,94,324,261,255,106,95,262,325,264,104,257,115,253,265,102,258,116,251,263,103,259,114,252,266,117,248,99,244,267,118,249,100,242,268,119,250,101,243,96,97,111,112,113,98,366,341,369,340,368,367,365,344,343,342,234,86,310,82,241,235,83,84,311,239,81,85,233,240,312,69,218,87,313,225,219,70,89,326,226,220,71,88,224,329,229,66,222,77,215,227,67,223,75,216,228,68,221,76,217,231,79,213,64,238,232,80,214,65,236,230,78,212,63,237,61,62,73,74,72,60,356,331,358,334,357,355,359,333,332,330 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#f17c3e64487a90443a3f1e09517d268af89a65f0705d71068edd4c3fc03a5700, 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 23:50:13 · history