Equation 677 Database

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Magma 92d3376426fb…

magma 92d3376426fb
Size
381
Isomorphism class hash
92d3376426fbe7ae4d7c45b3c28d4192ac219f2f3caa6cee8ca2fcd785cd44b7
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 23:16:54
Display reorder
380,320,319,321,322,323,318,151,156,160,165,141,146,29,30,25,26,27,28,135,266,276,291,175,171,196,200,205,181,186,191,36,31,32,33,34,35,45,255,270,285,43,44,211,216,221,226,230,235,241,246,251,262,280,295,38,39,40,41,42,37,24,23,19,20,21,22,341,342,340,356,360,347,351,370,375,365,316,315,317,312,313,314,152,157,162,167,142,147,100,101,96,97,98,99,137,267,277,292,177,172,197,202,207,182,187,192,107,102,103,104,105,106,95,258,273,288,93,94,212,217,222,227,232,237,242,247,252,260,283,297,90,91,92,87,88,89,2,0,3,4,5,6,337,343,334,358,362,345,353,372,377,368,327,326,328,329,324,325,150,155,161,166,140,145,78,79,80,75,76,77,136,265,275,290,176,170,195,201,206,180,185,190,81,82,83,84,85,86,68,257,272,287,66,67,210,215,220,225,231,236,240,245,250,261,281,296,61,62,63,64,65,60,69,74,70,71,72,73,331,333,336,357,361,346,352,371,376,367,300,301,302,303,304,305,153,158,163,168,143,148,56,57,58,59,54,55,138,268,278,293,178,173,198,203,208,183,188,193,18,13,14,15,16,17,1,256,271,286,46,47,213,218,223,228,233,238,243,248,253,263,282,298,7,8,9,10,11,12,51,50,52,53,48,49,335,332,339,359,363,348,350,373,378,366,308,307,309,310,311,306,154,159,164,169,144,149,131,132,133,134,129,130,139,269,279,294,179,174,199,204,209,184,189,194,108,109,110,111,112,113,120,259,274,289,121,122,214,219,224,229,234,239,244,249,254,264,284,299,116,117,118,119,114,115,126,125,127,128,123,124,330,338,344,355,364,349,354,374,379,369 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#09de7e296fafc11e1910887718202808c6591641f036fb4e85591d955a2aaea1, 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 23:16:55 · history