Equation 677 Database

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Magma 31808e11cbc5…

magma 31808e11cbc5
Size
381
Isomorphism class hash
31808e11cbc5f684cb12e54a35ca8ceaaf95c6377a372a3b92476e99c2bd42f8
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 23:21:00
Display reorder
380,161,160,156,157,158,159,295,246,256,266,276,286,260,270,280,290,240,250,166,167,162,163,164,165,201,211,221,231,181,191,120,121,122,123,124,125,83,78,79,80,81,82,317,312,313,314,315,316,74,75,76,77,72,73,130,131,126,127,128,129,216,226,236,186,196,206,364,372,344,345,376,357,332,352,367,358,87,86,88,89,84,85,292,243,253,263,273,283,262,272,282,291,242,252,91,92,93,94,95,90,202,212,222,232,182,192,173,168,169,170,171,172,51,52,53,48,49,50,323,318,319,320,321,322,57,58,59,54,55,56,174,175,176,177,178,179,213,223,233,183,193,203,369,371,342,341,373,346,331,359,360,347,142,141,143,138,139,140,296,247,257,267,277,287,265,275,285,294,245,255,133,134,135,136,137,132,205,215,225,235,185,195,30,31,32,33,34,35,36,37,38,39,40,41,308,309,310,311,306,307,43,44,45,46,47,42,26,27,28,29,24,25,217,227,237,187,197,207,365,375,340,339,377,353,338,337,363,354,21,20,22,23,18,19,298,249,259,269,279,289,264,274,284,293,244,254,15,16,17,12,13,14,204,214,224,234,184,194,71,66,67,68,69,70,107,102,103,104,105,106,329,324,325,326,327,328,98,99,100,101,96,97,64,65,60,61,62,63,219,229,239,189,199,209,368,374,348,349,379,336,343,333,362,335,1,5,0,2,3,4,299,241,251,261,271,281,268,278,288,297,248,258,9,10,11,6,7,8,208,218,228,238,188,198,108,109,110,111,112,113,147,148,149,144,145,146,303,304,305,301,300,302,153,154,155,150,151,152,118,119,114,115,116,117,210,220,230,180,190,200,361,378,356,355,370,330,351,350,366,334 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#3136fd46544160d7110a12defb5eea5a4c1d4e69d8e8a4280fa062cfc3b165d6, M = {72} 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 23:21:01 · history