Equation 677 Database

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Magma 33f82efa9e0b…

magma 33f82efa9e0b
Size
381
Isomorphism class hash
33f82efa9e0bd67de2244255a854e8c7eecc68a5e53556fe2415eeac505f6258
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 23:36:21
Display reorder
380,302,240,99,266,112,113,241,300,100,264,111,265,316,242,101,98,249,324,257,116,250,96,312,255,114,251,97,256,301,115,258,248,117,253,107,246,259,118,254,105,260,247,119,252,106,90,103,267,244,262,91,104,268,245,263,92,102,269,243,261,94,95,110,108,109,93,362,335,339,360,361,337,364,336,363,338,310,150,13,174,26,24,152,320,14,175,25,176,319,151,12,9,160,309,165,27,161,10,318,166,28,159,11,167,308,29,169,156,1,164,18,157,170,0,162,19,168,158,2,163,20,4,17,178,155,173,5,15,179,153,171,3,16,177,154,172,8,6,21,22,23,7,376,354,353,379,375,351,378,350,377,352,321,229,60,224,73,74,230,325,61,222,72,223,303,228,62,87,238,304,215,77,239,88,327,213,75,237,89,214,317,76,216,234,78,211,68,235,217,79,212,66,218,236,80,210,67,82,64,225,233,220,83,65,226,231,221,81,63,227,232,219,86,84,71,69,70,85,372,345,349,370,371,347,374,346,373,348,329,181,40,204,53,51,182,314,41,205,52,206,315,180,39,36,190,323,195,54,191,37,328,196,55,189,38,197,322,56,199,186,58,194,45,187,200,59,192,46,198,188,57,193,47,31,44,208,185,203,32,42,209,183,201,30,43,207,184,202,35,33,48,49,50,34,355,334,333,359,356,330,358,331,357,332,307,292,133,279,124,125,293,313,134,277,123,278,306,291,132,129,276,311,288,137,280,130,305,289,135,281,131,290,326,136,294,273,141,282,145,274,295,142,283,146,296,275,143,284,144,148,139,285,299,271,149,140,286,297,272,147,138,287,298,270,128,126,122,120,121,127,369,342,341,367,368,344,366,343,365,340 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#95709784173c62166e0281107140dd53c0e7c31d22d3a5dbc25d4f33f2e58a2e, 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 23:36:22 · history