Equation 677 Database

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Magma 232f88622adc…

magma 232f88622adc
Size
381
Isomorphism class hash
232f88622adcfbb5310a963d34bd5808ddb1072000873e27dad6f616f19ec39a
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 23:30:15
Display reorder
380,176,150,172,167,154,168,159,158,313,177,151,174,173,165,155,169,178,160,156,311,179,175,152,171,166,153,170,161,157,312,316,124,138,137,120,146,133,147,128,129,130,125,314,139,135,121,144,134,148,126,131,123,315,140,136,122,145,132,149,127,141,142,164,162,163,143,369,348,358,379,356,359,335,355,375,357,115,92,111,106,93,110,101,97,327,119,90,116,112,107,94,108,117,99,98,322,118,114,91,113,105,95,109,100,96,325,321,63,80,76,62,85,72,89,67,71,69,64,329,78,77,60,86,73,87,68,70,65,319,79,75,61,84,74,88,66,83,81,103,104,102,82,340,337,370,339,363,349,364,372,338,373,52,57,48,43,30,47,38,34,320,56,58,53,49,44,31,45,54,36,35,317,55,51,59,50,42,32,46,37,33,318,326,1,17,13,27,22,9,26,4,8,6,0,323,15,14,28,23,10,24,5,7,2,324,16,12,29,21,11,25,3,20,18,40,41,39,19,374,366,365,343,351,342,367,334,350,341,199,204,195,190,208,194,185,181,303,203,205,200,196,191,209,192,201,183,182,304,202,198,206,197,189,207,193,184,180,302,328,220,234,233,216,211,229,215,224,225,226,221,301,235,231,217,212,230,213,222,227,219,300,236,232,218,210,228,214,223,237,238,187,188,186,239,344,354,353,377,352,347,345,368,378,346,278,283,274,297,287,270,292,288,309,279,284,276,275,298,285,271,280,293,289,310,281,277,282,273,299,286,272,291,290,308,306,257,240,267,253,248,266,249,258,262,263,255,307,241,268,254,246,264,250,259,261,256,305,242,269,252,247,265,251,260,243,244,294,295,296,245,362,331,330,333,336,332,371,376,361,360 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#629ab6341cd973980cbbd61496a9220b9a2ad2f6cbea16f417813914f777cc43, 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 23:30:16 · history