Equation 677 Database

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Magma 8b7749152700…

magma 8b7749152700
Size
381
Isomorphism class hash
8b7749152700a5db25332cf41e97215f8484caa2ea7e788fd3fb958674602f3f
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 23:46:40
Display reorder
380,322,169,161,130,142,143,160,144,131,170,159,323,194,186,77,87,95,185,84,90,184,195,219,321,211,104,115,210,117,118,105,209,220,240,248,69,70,319,241,60,61,51,239,225,320,273,266,10,1,19,20,265,11,264,251,290,35,39,37,289,298,318,291,38,36,276,340,341,366,364,343,367,342,368,365,344,326,167,166,146,138,147,165,139,137,173,172,324,192,191,85,79,86,190,80,97,197,198,217,325,216,121,111,215,122,112,110,222,223,245,247,72,53,329,246,71,65,66,226,230,327,272,271,21,16,22,3,270,15,250,255,295,41,40,43,275,297,328,296,44,42,280,346,347,373,371,349,374,348,370,372,345,316,151,174,145,148,135,171,136,149,164,163,317,176,199,96,88,82,196,93,99,188,189,201,315,224,119,123,221,108,109,124,213,214,249,232,64,55,313,231,50,74,73,243,244,314,257,256,0,23,14,5,274,24,268,269,299,48,47,45,293,282,312,281,46,49,294,353,354,375,378,351,376,350,377,379,352,304,156,168,127,140,133,155,132,141,162,150,305,181,193,75,81,78,180,76,94,175,187,206,303,218,116,113,205,106,120,114,200,212,235,236,63,68,300,229,58,52,67,227,242,302,261,254,8,17,13,18,260,2,252,267,285,32,27,34,277,286,301,279,25,33,292,337,338,363,361,330,356,339,369,362,332,310,154,152,128,126,129,157,125,134,153,158,311,179,177,98,92,89,182,91,83,183,178,204,309,202,102,100,207,103,101,107,208,203,237,228,54,56,307,233,59,62,57,238,234,308,253,258,9,7,4,6,262,12,263,259,287,31,30,28,288,278,306,283,29,26,284,336,331,357,360,334,358,333,359,355,335 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#de5f29832587081214b202cf18f768c85cf1ddb2176eed0f01f35796195617d9, 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 23:46:41 · history